Harry Kane turned the ball into his own net in the 82nd minute as the hosts, who managed just a single shot on target, grabbed a scarcely deserved point.
It seemed Tottenham would claim the spoils when Christian Eriksen put them 2-1 up three minutes into the second half after Adam Johnson had cancelled out Nacer Chadli's opener.
But Pochettino was ultimately left to contemplate what might have been.
He said: "I am very disappointed, the players too. We played very well and created a lot of chances.
"I think we were unlucky because of the last goal that we conceded. This is football; you need to kill the game off."
Pochettino was not concerned by Tottenham's profligacy in front of goal, although he was far from happy with his men conceding just after taking an early lead.
He added: "I am not worried because the most important thing is to create chances. We just need to be more solid.
"When you concede a first goal like we did after you have scored early, you have to be smarter. It was easy for them to score."
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