Spurs would have climbed above Arsenal and Manchester City had they sealed victory in the weekend's early kick-off but instead it was Bournemouth who came closer to snatching all three points.
The Cherries were faster and more aggressive at the Vitality Stadium and Tottenham were fortunate to finish the game with 11 men after Moussa Sissoko's elbow caught Harry Arter in the face and Erik Lamela risked a second yellow card with a late challenge on Dan Gosling.
It means a second consecutive stalemate for Tottenham after Tuesday's draw against Bayer Leverkusen in the Champions League, and Pochettino admitted his side lacked their usual energy.
"Bournemouth pushed us a lot and we felt not fresh from the beginning of the game," Pochettino said.
"Our start was a bit sloppy and you can feel the team wasn't fresh
After 15 minutes we started to manage the game and it was under control.
"In the second half we were much better than Bournemouth and in the end you must score if you want to win the game.
"I am very pleased after playing Champions League in Leverkusen and before at West Brom, two very tough games, and to play a third game here, I am very pleased with the effort."
Sissoko, who came on as a substitute in the second half, sparked a scuffle when his elbow hit Arter in the face but while referee Craig Pawson consulted his linesman, no further action was taken.
The Frenchman could yet face retrospective action from the FA and a three-match ban for violent conduct.
"I need to see it (the Sissoko incident) now on the replay
Live it doesn't look bad but from my position it was difficult to see the reality," Pochettino said.
"In the first 20 minutes we arrived a little bit late because we weren't fresh and maybe we made some bad tackles and deserved the yellow cards.
"It wasn't bad intentions, it was because we felt a little bit tired from the beginning."
For Bournemouth, this was another encouraging display that means Eddie Howe's side have now taken eight points from their last four games.
Jack Wilshere also completed his first 90 minutes at club level since September 2014 and Howe was full of praise for the on-loan Arsenal midfielder's performance.
"I thought Jack was excellent today," Howe said
"First and foremost from a defensive perspective, he supported Callum Wilson superbly in our pressing
He did a lot of unseen work off the ball, competed well for second balls, all the niggly things you have to do to try gain control of the game.
"With the ball I thought he had a greater influence as the game went on and towards the end made a couple of really telling passes.
"The fact he stayed on was because his performance warranted it
His fitness levels have improved to the degree where he was able to deliver that."
Source : PA
Source: PA