PSG was 3-0 winner against the Ligue 1 leader as it was in action for the first time since a weekend defeat to Nantes that was disrupted by burglaries at the family homes of Angel Di Maria and Marquinhos.
Di Maria was substituted in that loss to attend to the matter, but both players were in the XI as goals from Mauro Icardi and Kylian Mbappe secured a quarter-final berth on Thursday (AEDT).
It was not an entirely convincing PSG display, as Lille had 18 shots to their 11 and Keylor Navas was required to save a penalty for the third time this season.
Pochettino was only interested in praise for his players and their families, however.
"Of course I'm so happy with the performance and the spirit of the team," the coach told the club's official channel.
"They deserve massive credit and I want to congratulate them but most of all the families because the last few days were very tough for everyone.
"We all feel what happened to Marqui and Angel. It really touched the group and that's why I want to congratulate the team, the players and the families suffering around them.
"I'm so happy. I think we fully deserved to go through to the quarter-finals and, in this difficult circumstance, I'm happy for the 3-0."
Di Maria had two shots and created a single chance, while Marquinhos contributed four tackles, five clearances and a block.
Navas was the star of the show, though, denying Yusuf Yazici from 12 yards with 12 minutes remaining.
Only Rui Silva and Oliver Baumann (both four) have kept out more penalties than Navas in all competitions this season among goalkeepers across Europe's 'top five' leagues.
"He is one of the best goalkeepers in the world," Pochettino said of Navas, who finished with five saves in all. "His level is incredible."