After Liverpool's earlier victory in the battle of Merseyside, it was crucial for Spurs and Villa, starting the clash in fifth and seventh respectively, to crank up the pressure on their rivals.
The hosts dominated the first half with goalkeeper Brad Friedel twice denying Ledley King, and a 30-yard thunderbolt from midfielder Tom Huddlestone.
Tottenham keeper Heurelho Gomes also impressed as he made a double save from James Milner and Gabriel Agbonlahor.
Spurs pushed for a winner with Peter Crouch's deflected shot going wide and Jermain Defoe denied a late penalty.
Both teams continue to boost an impressive array of statistics. Villa are unbeaten in eight and Spurs with five successive clean sheets at White Hart Lane, but one point is a prize neither team will fully appreciate.
Only one team seemed determined to push for all the spoils with Crouch twice going close in the final minutes and Defoe failing to get a penalty award after a tackle from Stilian Petrov.
LONDON (AFP) - Harry Redknapp insists the race to finish in the top four is wide open after Tottenham blew their chance of reclaiming fourth spot in a 0-0 draw with Aston Villa on Saturday.
Redknapp's Spurs side had been pushed down to fifth spot following Liverpool's victory over Everton and their failure to overcome Aston Villa at White Hart Lane means they now sit one point behind Rafael Benitez's side.
Villa sit two points further back having drawn level with sixth placed Manchester City who unexpectedly lost at Hull City.
Redknapp, who believes that only Manchester United and Chelsea are guaranteed to qualify for next season's Champions League, believes there will be many more twists and turns in the battle to qualify for Europe before the end of the season.
"Obviously it was a big result for Liverpool," said the manager.
"They ground out a result, it's their weekend this week, it will be somebody else' s next week, somebody else's the week after.
"Of course it's going to be tight, it's going to go all the way to the wire. You didn't see Manchester City getting beat at Hull today, not many people would have tipped that one, would they?"
O'Neill echoed Redknapp's thoughts although he believes Liverpool's move up to fourth could be a sign the Anfield club are over the problems that dogged them during the first half of the season.
"What Harry said is absolutely correct in that nobody would have expected Manchester City to get beaten there today (Saturday)," said the Villa manager.
"I think it's somebody's week this week. We are hanging in, today was a big point for us away from home.
"We've got 14 games left in the league and I can't look past Manchester United on Wednesday night.
"I never felt Liverpool were out of it, because it's Liverpool."
O'Neill hailed his side's defensive efforts in securing a scoreless draw against Spurs and believes the display demonstrated that his players have not been distracted by the looming League Cup final appearance.
"It probably is as good a defensive performance as we have had," he said before singling out keeper Brad Friedel for special praise.
"I think Brad has been reinvigorated with the arrival of young Brad Guzan. The two Americans coming together, there's a bit of competition and I just think that Brad has been exceptional. In the last number of weeks his performances have been terrific.
O'Neill's main concern is whether his squad can meet the demands of challenging in the league, the League Cup and the FA Cup. Emile Heskey limped out of the Spurs game after 21 minutes with a groin problem while Nigel Reo-Coker is a long term casualty.
"We are in the League Cup final which we will try and think about the week beforehand," said O'Neill.
"We've got Manchester united on Wednesday. I must admit I have gone with the same side for a number of weeks now. Nigel Reo-Coker will be out for about ten weeks which will be a real blow for us so we will need everybody around in the squad.
"I remember Alex Ferguson saying to me before we played Manchester United up there he was pretty amazed that we've gone with the group of players. I' m hoping that their enjoyment of playing and of wanting to play will stand them in good stead over the coming months. But I don't know."