The north Londoners moved to within a win of the Europa League knockout stages after condemning the Greeks to a first ever home defeat in continental competition.
Up until half-time it had looked like a scoreline similar to the 5-1 win of a fortnight ago was on the cards, with Andros Townsend and Harry Kane turning Spurs' possession into goals.
However, Pochettino's side almost undid that good work with a shocking, error-riddled second half in which Asteras had 14 efforts of differing quality.
The hosts managed to find the net late on through Jeronimo Barrales, scoring from the spot after a foul which saw Federico Fazio sent off - but Spurs held out for a 2-1 win.
"I think that during the first half we were better than Asteras," Pochettino said after the Group C clash
"We played well during some moments and scored two goals
"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 because Asteras start to play and to be confident in the game
"They created some chances and at the end with the Fazio penalty and him being sent off, it made it difficult in the last four or five minutes - but we are happy
"We came to get the three points, the result is good and I am happy."
Pochettino was surprisingly calm and upbeat given his side's second-half collapse
The Spurs head coach had been angered by his side's lax defending towards the end of the reverse fixture against Asteras - a performance compounded days later by Newcastle coming from behind to win 2-1 at White Hart Lane
Tasos Tsokanis' strike seconds into the second half here was worryingly reminiscent of Sammy Ameobi's game-changing goal for the Magpies, as was their inadequate response to the increased pressure
Put to Pochettino that he was surprisingly chipper considering the display, he said: "Today Asteras didn't score at the beginning of the second half
It is a different game
"We need to improve, we need to work, we need to realise we need to improve in different aspects of the game
"I think that we played very well but the second half was different and we need to review the game and improve."
The second-half display would seem to give credence to England coach Gary Neville's recent comments that Spurs are "weak" mentally - comments Pochettino still does not agree with
"If you have a weak mentality, it would be there in 90 minutes, not only in some moments in the game," he said
"The only thing is you need to show you are ready for 95, 96, 97 minutes in the game - it's true, it's true
"We need to improve, we need to work hard
I explained after the game with Newcastle that we need to work very hard with our mentality to be focused on the game for 95 minutes
"It is one aspect that we need to improve, but it is hard to work because it is a difficult aspect to improve in football."
The defeat was Asteras' first at home in three seasons of European competition, but manager Staikos Vergetis was proud of their display in the biggest match in the club's history
"Tonight we had a very difficult game against a very strong side," the Tripoli native 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."
Source : PA
Source: PA