With no prize of a Cup Final at stake, the spark and desire were missing from a game that was so important to both teams for different reasons.
Spurs are badly in need of points to take them out of the bottom half of the table and up where they feel they belong and the Blues needed three points to cement the fourth-placed Champions League spot after Liverpool lost at West Ham United.
A very cagey start to the game saw little or no chances for both sides in the first 15 minutes but it was the home team that pushed forward as they tried to test the new-look Spurs back line.
The first chance of the game saw Everton left back Nuno Valente charging down the wing to whip in a cross to Victor Anichebe who nodded the ball to strike partner Andy Johnson who was just unable to tap home.
The Blues started to turn the screw and the deadlock could have been broken if not for some last-gasp defending from the new signing Jonathan Woodgate.
Neat footwork by Leighton Baines carved himself a shooting opportunity but the quick reactions of the former Real Madrid man saw him block the strike as he prevented an almost certain opener.
With Lee Carsley sat in front of the Blues' back line, the formidable partnership of Robbie Keane and Dimitar Berbatov were kept quiet in the first half and, apart from a couple of routine catches, Everton's shot-stopper Tim Howard didn't have a save to make.
Johnson had a penalty claim turned down as a trip in the box had the crowd screaming for blood, but the referee waved play on.
TV replays showed the centre-forward had tripped over his own quick feet.
The second half started brightly for the home side as, within the first two minutes, Mikel Arteta took the ball off the feet of Johnson and jinked his way through the defence but an acute angle could only see Arteta's ball fly across the face of goal.
Almost immediately, the visitors were handed a chance as Everton skipper Phil Neville lost the ball on the edge of his box which was threaded through to Keane by Berbatov but Howard kept his concentration to pull off a smart save.
The best opportunity of the match fell to Johnson on 59 minutes after some fine work by Manuel Fernandes found him inside the box with only the keeper to beat but a low shot was saved by the underside of keeper Radek Cerny's body and cleared to row Z by Woodgate.
Tottenham had a chance to win the game with only six minutes left when pocket rocket Aaron Lennon flew down the wing and drilled the ball along the edge of the box.
Berbatov's shot was bravely blocked by the lunging Phil Jagielka to save a point for the home side.