The Baggies looked on course for their third victory of the season at the Hawthorns after former Spurs forward Nacer Chadli broke the deadlock after 82 minutes.
But they were denied the full three points by Dele Alli, who found the bottom corner inside a packed penalty area with just one minute of normal time remaining.
That came after goalkeeper Ben Foster had thwarted the visitors time and time again, denying Alli, Christian Eriksen and Ben Davies with some fine saves as he kept the Baggies in the game in the first-half.
Alli's equaliser meant that West Brom have drawn 1-1 for the third successive Premier League game but despite that, Pulis felt his team did well to produce an improved second-half display.
"We gave Spurs a better game in the second-half"
Pulis acknowledged in his post-match press conference that his team had Foster "to thank" for keeping them in the game and admitted that "half a dozen of the players" still seemed that they were away on international duty.
"We never got up to the ball. We allowed Tottenham to play," he said, also talking about how Mauricio Pochettino's men "played in a different way" and were "very, very clever" in their play.
The West Brom boss felt that his side were "stretched" as Spurs "got Eriksen and Alli in the little pockets", insisting: "That caused us a few more problems, but we managed to work it out second-half. I thought we gave them a better game in the second-half."
On what he spoke to his players about at the break, he said to journalists: "Just the pockets. We were getting caught in midfield where we were just not marking people. We were filling spaces and Spurs were playing outside the spaces we were filling."
The 58-year-old added that his side needed to "sort that out" and "got that done", and as a result he felt that the Baggies' performance was "much better" and they "got closer to them and caused them much more problems."
He felt that the second-half was "more of an even contest" after the opening period which he declared was "definitely more difficult" for the home side.
Tottenham are one of the best teams in Europe - Pulis
Pulis was also particularly satisfied given the quality of the opposition, as he explained: "Watching them today, Tottenham are an absolutely fantastic team. They're one of the best teams in Europe, never mind in England."
He called it "wonderful" to be able to watch a team like Spurs, citing their array of "talent and players they've got", and insisted that should not be taken for granted as it can be in the Premier League.
"It's a wonderful league to be in and as soon as you take your eye off the ball, think you're better than you are and start becoming complacent, the bottom drops out," Pulis continued.
He added that there are "a lot of clubs in the Championship who have done that" and insisted West Brom must "keep its feet firmly on the ground" and "try and improve in every window."
Boss praises "real quality" Chadli goal
Pulis was also delighted by the finish of Chadli, suggesting that he won't get the credit that he should for the goal.
He lauded Hugo Lloris for a "great save" to initially push James McClean's volley on to the post, and said that the goalkeeper "got up so quick" that Chadli only had "the top half of the goal to hit."
"It's a little square if you look at it and the kid sticks it in there," Pulis added, calling it a "real, real quality finish" from the Belgian, who joined from White Hart Lane for £13 million in the summer.
Pulis hopeful Brunt can return to full fitness
The game also saw the return of vice-captain Chris Brunt after an eight-month absence due to a knee injury.
Pulis applauded the midfielder for having "done well" to recover, insisting he has "the quality" that West Brom need. He also said: "Hopefully now he can get fit and get a run of games and help us through what is going to be a tough season."