Spurs triumphed 1-0 thanks to Eric Dier's eighth-minute goal but did so in front of an official attendance of 43,268 - some way short of the national stadium's 90,000-seat capacity.
Pochettino was seen to point to an almost completely empty upper tier ahead of kick-off, seemingly taken aback by the low turnout on a rainy afternoon in the capital.
"I was a little bit surprised that it was empty," he told a news conference. "But I understand that this is difficult – we cannot ask for more from our fans. Of course, it was a difficult day with the weather and everything and it's not easy.
"I am always honest and I was surprised that the top tier was empty."
Spurs were not at their best as they struggled to build on their early opener and had to withstand sustained periods of pressure from their spirited visitors, who at times looked capable of snatching an equaliser.
"It wasn't the best performance," admitted Pochettino. "We fully deserved the victory and the three points and in the end that's the most important thing because it keeps us in a very good position in the table, one point off the top.
"But of course we want to be in the same position at the end of the season, or be a contender. I think we need to improve a lot in our performance.
"We play after the defeat to Barcelona [on Wednesday] and this was difficult, but I'm happy because of the victory. I think we can play better and we need to play better if we want to be a contender for the top four.
"It was a game that that looks like it's going to be an easy afternoon and at the end it's so complicated because, if they score from a set-piece, maybe we are talking in a different way now.
"We need to improve a lot. We need to kill the games, have more control, more calm when you play at home.
"The effort was fantastic and it was not easy after the defeat against Barcelona to be ready again to compete, but I think we competed well."