Spurs went above neighbours Arsenal after their surprise 2-1 home defeat to Watford, but could not move any closer to the table toppers after Antonio Conte’s team drew 1-1 at Liverpool.
The Sunderland stalemate comes after Spurs 2-2 draw with Manchester City and a narrow 4-3 win over Wycombe in the FA Cup at the weekend.
Speaking at a post-match press conference, Pochettino said it was points dropped.
"Not frustrated – disappointed. It was a massive opportunity to reduce the gap to Chelsea, be in second position which was important for us," he said. "When you drop two points like tonight, it's difficult to change the feeling. We feel bad, that's the reality.
"First half, we didn't play well – we were poor. We shot once, it's difficult to win a game in that way. Second half we were much better, we created some chances to score but it wasn't enough. We dropped two points, we feel disappointed but not only with the result, with our performances – we only competed for 45 minutes in the second half.
— Tottenham Hotspur (@SpursOfficial) February 1, 2017
"Man City was the same, Wycombe with different players we struggled too. In the same way, we started the game today. It's a thing to improve, to analyse for the future. It's clear something is wrong from the very beginning in the last few games."
Pochettino refused to criticise the referee after Sunderland's Jack Rodwell failed to be sent off for a nasty challenge on Mousa Dembele.
"There is nothing to say, nothing to complain about. That is football. For the referee, it is difficult to take a quick decision. I think we need to support the decision of the referee and it's important," he said.
"It wasn't the type of decision that can change my opinion, we were poor in the first half and second half we were better but it was not enough to get the three points. But on the tackle, that is football."