Spurs had previously drawn 1-1 with West Bromwich Albion and 0-0 with Bayer Leverkusen.
Tottenham Hotspur manager Mauricio Pochettino admitted he is "concerned" after three successive draws called into question his squad's ability to stay the course in the Premier League and Champions League.
He acknowledged his players were not "fresh" in Saturday's goalless draw away to Bournemouth, which cost them the chance to top the Premier League table, especially in a sluggish opening 15 minutes.
Spurs had previously drawn 1-1 with West Bromwich Albion and 0-0 with Bayer Leverkusen, costing them momentum on both the domestic front and in Europe.
"Yes, we are concerned," Pochettino said. "It's true we need to improve if we want to be a real contender. It's true after two games away at West Bromwich and Bournemouth, you must win at least one.
"But when you analyse the whole situation, we have to give value to the point because the effort was fantastic. We had some injuries. So I am happy.
"The game was very competitive and very tough. Bournemouth pushed us a lot, but we were not fresh from the beginning. Our start was very sloppy, but after 15 minutes we started to manage the game."
His defence coped adequately without the injured Toby Alderweireld, but the continued absence of Harry Kane and his ability to create and convert chances meant that Tottenham's goal threat was restricted largely to shots from range.
The news that Kane, who scored five goals against Bournemouth in two victories last season, is "not far away" from a full recovery from his ankle injury was encouraging, if vague.
"I'm very pleased after we played in the Champions League and before that in West Bromwich, two tough games, because the players made a very big effort," said Pochettino.
"But we missed the freshness to be sharp in the last third. Second half we dominated, but it was more difficult to create chances to score."
Pochettino said he did not see an incident in which substitute Moussa Sissoko caught Bournemouth's Harry Arter in the head with his elbow, which left home fans calling for a red card.
But he admitted that fatigue had contributed to four first-half yellow cards that left Jan Vertonghen, Danny Rose, Erik Lamela and Delle Alli one careless lunge from being sent off.
"We didn't show the freshness where you can anticipate the action," he explained.
"We made some bad tackles. Maybe we deserved the yellow cards. But it wasn't bad intention, it was because we felt tired at the beginning."
Pochettino paid tribute to Bournemouth's game plan, which involved doing to Spurs what they usually do to opponents: press high up the field and beat them for energy and effort.
"I was really proud of the players today," Bournemouth manager Eddie Howe said.
"Probably more proud than I was this time last week (when Bournemouth beat Hull City 6-1), partly because of the quality of the opposition we were playing against.
"Our game plan was to disrupt their rhythm, their normal way of playing. They're supremely talented players and we felt our best option was to stop the ball getting into the final third with our work rate and intensity.
"That's easier said than done, but the players delivered an incredible physical performance, full of endeavour and desire."
On the topic of physical performance, Jack Wilshere, on loan to Bournemouth from Arsenal, completed the full 90 minutes for the first time in two seasons.
"I kept him on because his performance warranted it," Howe said. "His fitness has improved to the point where he is able to deliver that."