The north Londoners moved a step closer to Europa League knockout stages with a 2-1 victory that condemned the Greeks to a first ever home defeat in continental competition.
Spurs looked to be heading for another sizable victory in the first half, with Andros Townsend and Harry Kane turning good possession into goals
But they were left with a nervy finish when Federico Fazio conceded a late penalty, and was sent off, allowing substitute Jeronimo Barrales to pull one back.
Pochettino said: “We need to realise we have to improve in different aspects of the game and work.
“We played very well in the first half but the second was different and we need to review the game and improve.
“After half-time, they started well and created one chance very early. We had some chances to score the third goal but in football it’s difficult when a team starts to play and to be confident in the game.
“We came to get the three points, the result is good and I am happy.”
The defeat was Asteras’ first at home in three seasons of European competition, but manager Staikos Vergetis was proud of their display.
“Tonight we had a very difficult game against a very strong side,” the Tripoli boss said.
“Our team put in a great performance. In the first half we had good defensive organisation, although Tottenham had control of the ball.
“We could have avoided the second goal after conceding the penalty, but in the second half we were on top.
“We are disappointed not to have scored earlier. We were very energetic and I want to thank every single player for their efforts.”
Tottenham are second in Group C behind Besiktas, with both sides on eight points, while Asteras sit third with four and Partizan, whom Spurs play at White Hart Lane in two weeks’ time, are bottom with a single point.