"I am so happy to win", Pochettino said.
The England forward has scored six goals in six games against Arsenal in the Premier League.
It was a performance that nearly earned outplayed Arsenal an unlikely point only for substitute Alexandre Lacazette to waste two last-gasp opportunities, the second when he was clear through on Spurs keeper Hugo Lloris but shot wide of the far post.
Arsenal's players shouted for a push on Koscielny; so did their manager Arsene Wenger, but the appeals smacked of desperation.
The first half was an exercise in defensive austerity, with both teams holding each other at bay for the most part.
Tottenham are coming off a hard-fought 2-2 draw with Liverpool, secured by a last-minute Harry Kane penalty, his 100th goal for the club, and a more routine 2-0 win against Newport County in an FA Cup fourth round replay on Wednesday.
"It's a game we couldn't afford to lose, of course", manager Wenger said.
The visitors were starting to look exposed at the back and Spurs wasted three chances on the break, with Son Heung-min blazing over the bar, Alli prodding wide when one-on-one with Cech and substitute Erik Lamela seeing an effort blocked wide at the right-hand post.
"We were caught by a super striker, he is one of the best in the world. he scores against everyone". Saying his thoughts on the comments of Pochettino, Wenger said that he wasn't sure if the Argentine apologized for the dive. Lacazette twice should have made them pay, volleying one chance over and then skewing an even better one wide when Davinson Sanchez got the wrong side. "Manchester United decided that once they were in the semi-final [last season], we are far from the semi-final. We can only look at ourselves", he added.
Kane, who missed two clear headers either side of his goal, was also delighted to see out the victory after Alexandre Lacazette spurned two late opportunities to equalise.
After leading Spurs to seven points from three games against their nearest rivals, however, there can be no doubt that Kane is among the very best all-round strikers.
Spurs restricted Arsenal to few clear-cut chances at Wembley today and they will need a similar performance in the Champions League on Tuesday night.