The Swiss champions were beaten by a stoppage-time goal when the sides met on matchday three, but Basel achieved a measure of revenge with two goals in each half on Tuesday.
The result moved Basel into second place in Group B on six points, behind Real Madrid, ahead of a trip to Anfield on matchday four.
"We had a lot of movement and have made good decisions," Sousa told the club's official website.
"There was a lot of passion in the game. I am very satisfied with the performance.
"I'm really proud of the team that they could implement the game plan.
"We have shown a fantastic performance, which has led us to the second place."
Captain Fabian Frei set up both first-half goals, sending teenage striker Breel Embolo through to score his first Champions League goal with a pinpoint througball and repeating the trick for Derlis Gonzalez soon after.
Embolo provided a wonderful cross for Shkelzen Gashi to make sure of the points after 59 minutes, with Marek Suchy rounding off the scoring from a corner.
"I'm glad the players have scored the goals from my passes," Frei told 20 Minuten.
"It was a tough game, but at 3-0 we could save some energy."
