Dele Alli sealed a late point to maintain their unbeaten run in the Premier League to eight games, their best start since 1990, with an 89th-minute equaliser.
That came after Nacer Chadli, who signed for West Brom from Spurs in the summer, had opened the scoring just seven minutes later with a powerful close-range finish high into the net.
Though Alli's late effort meant the North London club are yet to taste defeat this season and are the only side who haven't lost in the top-flight, Pochettino felt his side could have come away with all three points from the Hawthorns.
But the manager also hailed the show of character from his side to respond to Chadli's breakthrough effort with a late goal of their own.
We were unlucky not to get the win, feels Spurs boss
Asked whether the draw felt more like a defeat than a victory, the Argentine admitted that it depends but added: "I am happy with the performance. It's true that we can talk about the need for us to be more clinical, but the team played very well in the first-half."
Pochettino hailed how his team "created a lot of chances" but felt "a little bit" disappointed at the manner that his side conceded, failing to follow in on Hugo Lloris' save from a James McClean volley.
However, he told reporters in his post-match press conference that his side "showed character" to earn a point, reiterating that he is "happy with the performance" and "very pleased" because he believes it is "always difficult" to face West Brom away from home.
"I think that today we haven't got the victory because we were a little bit unlucky, and because of Ben Foster too," continued Pochettino, who insisted the 33-year-old was Man of the Match for the saves he made in the opening period.
Pochettino's men could have leapfrogged table-toppers Manchester City with a win as Pep Guardiola's men drew at home to Everton, but Pochettino says his side must still be pleased to have drawn in the circumstances.
He acknowledged that they "missed the opportunity" to "pick up the three points" and said they "missed two" before insisting: "But in the same way I think it was a very difficult and physical game."
The manager bemoaned the wastefulness of his side in front of goal, saying that given they were "much, much better" in the first 45 minutes and had "nearly 80 per-cent possession" as well as "five or six big chances", they should have scored so as not to "leave open the score for the other team" in a league which is "always difficult."
Pochettino reflected on their previous meeting with West Brom towards the end of the previous season and said his side are now "more mature", adding: "I think that today was a good message. We are more mature and the team after we conceded showed the character we need. That is important."
Pochettino: Alli a key player to my Spurs side
The manager was asked about the persistance shown by goalscorer Alli, who fired the decisive goal having earlier missed a gilt-edged one-on-one opportunity in the first-half.
Pochettino insisted he was happy for Alli to have gotten on the scoresheets but said that the 20-year-old "needs to improve" because he "must score" what he called "a big chance."
Nevertheless, he said that Alli is "a good player" and "an important player" and expressed his delight and pride that the team showed their strong mentality to get back into the game when "there wasn't too much time left."
He called it the "most important thing" that they maintain consistent performance levels, having beaten Manchester City 2-0 before the international break when Pochettino felt they "played very well."
He also called it "important" that they are "still unbeaten" and cited the impact it will have on his side's confidence going into their next few fixtures, with "a lot of games ahead."
Alderweireld a major doubt for Leverkusen clash
But one major worry coming out of the draw in the West Midlands is the possibility of losing key centre-back Toby Alderweireld for an extended period after he was stretchered off on the hour.
The Belgium international appeared to collide with compatriot Jan Vertonghen and could not continue despite his attempts.
Pochettino admitted that it currently is "very difficult" for Alderweireld to recover in time for their trip to Bayer Leverkusen in the UEFA Champions League on Tuesday.
He said they "need to assess" the defender, who has thus far appeared in every league games of Spurs' season, explaining that they "must wait a little bit" and "see what happens" because they "don't know what the problem is."
Pochettino revealed: "Now, the injury is very painful in his leg. He feels a lot of pain but we don't know [what it is]. We need to assess it tomorrow and then give it time, be it 24 hours or 48 hours. We will do the scan or whatever the doctor wants to do. We need to give Toby one or two days to be clear on what happened to his leg."
The Tottenham boss admitted he hadn't had much chance to ask Alderweireld about his injury and said it was "difficult" for him to view it from the bench, so could not offer any insight on whether it was an impact injury or one sustained by a bad landing.
He could however add: "The injury is [across] a big area. Knee, leg, all of it. It's big area in which he feels the pain."