The Premier League side were in complete control by half-time of Thursday's clash, as first Andros Townsend scored from the penalty spot before turning provider for Harry Kane to head home a second before half-time - the striker's 10th goal in all competitions this season.
However, Asteras made life difficult for Spurs in the second half as Diego Rolle and Facundo Parra wasted great chances, while Pablo Mazza saw a shot cannon off the post.
The Greek side were rewarded in the closing stages when substitute Jeronimo Barrales scored from the penalty spot in the last minute after being fouled by Federico Fazio, with the centre-back shown a straight red card for the offence.
Despite the Jekyll and Hyde nature of Tottenham's performance, Pochettino was happy to travel back to London with three points and the knowledge victory over Partizan in their next Group C match will book their place in the knockout stages.
"In the first half we were the better side and scored twice," he said. "In the second half they started well.
"We came here to get the three points and we got the result.
"We knew it would be difficult so it's a good win. The first half was very good but in the second half we needed to be more solid.
"The most important thing is three points. If we beat Partizan we are through to the next round."
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