Everton manager Roberto Martinez expects Arsenal to follow suit and drop points in the scramble for fourth place in the Premier League.
A 3-2 defeat against Crystal Palace at Goodison Park on Wednesday means Everton passed on the opportunity to leapfrog back over Arsenal – who beat West Ham 3-1 24 hours prior - into fourth in the battle to secure qualification to next season's UEFA Champions League.
With four league games remaining, Arsene Wenger's men will secure a top-four finish if they match Everton's results over the coming weeks.
And Martinez has cranked up the pressure by suggesting that the London club will not win all their remaining fixtures, insisting his Everton side, a point further back, will fight to the end.
"We have 12 points to play for," the Spaniard said.
"We are close to fourth place and we are still in a good position.
"I don't think Arsenal will take maximum points from their remaining games.
"If you looked at the start of the season, it's a magnificent position.
"The way we finished the second half gives me great optimism we can finish the season strongly."
Goals from Jason Puncheon, Scott Dann and Cameron Jerome prevented Everton from making it eight home league wins in a row.
Steven Naismith and Kevin Mirallas netted for the hosts to make it 2-1 and 3-1 respectively.
Martinez knows it is a fixture that Everton were tipped to win, but paid tribute to a plucky Palace performance.
"The result is a hurtful one because of the expectation that we had and the desire that we brought into the game," he said.
"In the first half we played with a bit of wanting to win so much that we forgot about simple basics. In the second half, it was completely different.
"We were positive and back to being ourselves.
"But in every aspect, the game played into Crystal Palace's hands. They were well organised, happy to sit behind and play on the counter and dead balls."
|Coach: Roberto Martínez|
for Gerard Deulofeu 46'
for A. McGeady 59'
for G. Barry 59'
|Monk slaps ´astronomical´ price on Bony´s head|
|Australian clubs looking at Ronaldinho|
|Sinclair enjoying ´one of the best pre-seasons´|
|Spiranovic surgery a success|
|Seattle Sounders 0 Los Angeles Galaxy 3: First-half blitz fires Californians to victory|
|Lemina thrilled with Bielsa effect|
|Bayern´s Green chomping at the bit|
|Palace complete US tour with easy win|
|Simeone: Atleti´s La Liga triumph was no fluke|
|Carragher: Liverpool didn´t want me|
|Sturridge: ´I´ll step up´|
|Van Gaal: Formation gives United flexibility|
|Mathieu insists age is no barrier|
|Martinez the deal sealer, says Besic|
|Coaches embrace blockbuster Serie A start|
|Ronaldinho to leave Atletico Mineiro|
|Lorient capture Ayew|
|Celtic loan Berget, sell Watt|
|Pires signs up for Indian Super League|
|Allegri set for early San Siro reunion in maiden Juve campaign|
|Bakayoko makes Monaco move|
|Bakayoko makes Monaco move|
|Lens granted Ligue 1 place|
|UEFA Champions League Preview: Red-hot Salzburg face Qarabag|
|Parma bring in Cassani from Fiorentina|
|De Vrij set for Lazio|
|BREAKING NEWS: Everton complete Besic signing|
|Kongolo pens Feyenoord extension|
|Redknapp confirms Granero exit|
|Advocaat confirmed as Serbia coach|
|CSL Preview: Henan aim to escape drop zone, Liaoning host Guangzhou RandF|
|Arribas makes Sevilla switch|
|Chambers joins Arsenal|
|Ospina buoyed by Arsenal recruitment|
|Liverpool´s loss is our gain, says Redknapp on Remy|
|Ferdinand: I would still be at United with Giggs in charge|
|Pepe targets Super Cup glory|
|Martinez prioritising striker signing|
|Perez not looking to leave Benfica|
|Klopp itching to work with full Dortmund squad|
|Mourinho: It feels like Drogba never left|
|FIFA asks for FIGC review into alleged racist remark|
|Hull to review Maguire deal|
|Wenger prepared to gamble on Chambers|
|Atletico agree Griezmann deal|
|Irvine planning further striker addition|
|Campbell: Black professionals scared to talk about racism|
|Mata backs Herrera to star in Premier League|
|Injured Rafael returning to Manchester|
|Schmidt demands more from Leverkusen|
|Copa Libertadores Preview: Defensor Sporting banking on home record|
|Remy´s Liverpool move off, confirms Rodgers|
|Inzaghi demands nastiness from Milan|
|MLS Review: Timbers triumph in Montreal, Dallas thwart Vancouver|
|Jovetic ready to lead City line - Pellegrini|
|Lewandowski impresses Ribery, Alaba|
|Colombian Primera A Review: Three clubs remain perfect, Atletico Nacional get off the mark|
|Rodgers: ´We can score goals´ without Suarez|
|Chilean Primera Division Review: Canales brace powers Universidad Chile|
|Atletico Madrid need penalties to edge past Earthquakes|
|Liga MX Review: Monterrey, America stay perfect|
|Paraguayan Primera Division Review: Capiata set pace|
|Brazilian Serie A Review: Cruzeiro win again, Kaka scores|
|Sterling goal sees Liverpool past Olympiacos|
|Peruvian Primera Division Review: Los Caimanes notch maiden win, Inti Gas claim top spot|
|CAF Champions League Review: Zamalek held, Vita Club leave it late|
|Jovetic at the double as Manchester City thrash Milan|
|Monk thrilled by Sigurdsson contribution|
|Lovren signs for Liverpool|
|Mourinho pleased with Olimpija test|
|Vertonghen eager to remain at Spurs|
|Sigurdsson marks Swansea return with a brace|
|Lewandowski, Rode help Bayern retain Telekom Cup|
|Immobile scores and suffers injury in Dortmund win|
|Costa scores on Chelsea debut|
|CAF Confederation Cup Review: Leopards de Dolisie 1 Real Bamako 2|
|Thai Premier League Review: Buriram pull clear, Police edge away from danger|
|Falcao nears Monaco return|
|CSL Review: Harbin Yiteng produce another upset, Evergrande stretch lead|
|Britton and Emnes to miss season-opener|
|Taylor-Fletcher strike sinks Everton|
|J.League Review: Chasing pack close on Urawa Reds, Tokushima Vortis secure rare win|
|Ancelotti expects fresh Bale to be even better|
|Simeone keen on Griezmann|
|Mazzarri refuses to set Inter targets|
|Lazio director targeted by fans|
|Dyche rules out Deeney move|
|Rummenigge: Bayern will never sack Guardiola|
|BREAKING NEWS: Arsenal to bring in Ospina|
|Pochettino quiet on Schneiderlin link|
|Vidic settling into Inter life|
|Van Gaal hints at Zaha United future|
|Di Maria will report for training - Ancelotti|
|Wilshere vows to answer critics|
|Rodgers expecting titles|
|Deila demands Celtic cutting edge|
|Rodgers: We won´t rush Lallana|
|Wenger: We have to be better against top-level teams|
|FIGC presidential candidate uses racist slur|
|MLS Review: Columbus claim second straight win, Toronto falter|
|Villa battle past Dynamo in Houston|
|United more efficient, says Garcia|
|Pedestrian Tottenham edge past Chicago Fire|
|Van Gaal bemoans display|
|CS Sfaxien 1 ES Tunis 0: Troussier era opens with a win|
|Icardi stars from the spot as Inter overcome Real Madrid|
|Arsenal upstaged by Red Bulls|
|Pre-Season Friendly Review: Rooney stars for United, Bayern reach Telekom final|
|In-form Rooney inspires Manchester United win|