Dortmund dominated possession for large parts of the game, but Tottenham showed a ruthlessness in front of goal to see off the Germans 3-1 in their Group H opener.
Harry Kane was once again in irrepressible form, scoring twice and setting up Son Heung-min for an early opener.
Andriy Yarmolenko scored a wonderful goal for Dortmund, who will feel hard done by after having two goals incorrectly ruled out for offside.
Tottenham travel to Cyprus in two weeks to play APOEL, and Pochettino is confident the performance against Dortmund will stand them in good stead for the rest of their campaign.
"It was so important to win, we are so happy," he told BT Sport.
"It was so important to start well in a tough game. Dortmund played really well, they dominated the first half. We increased our level in the second half and we were very clinical in front of goal.
"It is more than three points. At half-time we fixed some problems and modified the position of some players. The tempo of the game decreased which was better for us. Dortmund are a very aggressive team, we struggled a little to pass the ball quickly.
"Sometimes you can't dominate, you have to play a different way and the team is more mature now. We can learn a lot from this game."