PSG reached the Champions League semifinals 5-4 on aggregate, having lost the second-leg 3-2 at Villa Park on Tuesday night. Hakimi struck as PSG jumped to a 2-0 lead inside the opening half-hour before Villa stormed back.
He said afterwards: "We weren't afraid.
"We knew we were going to suffer and we suffered because of ourselves but we are happy to have preserved the qualification.
"We see the work we are doing with the coach, it shows in the results and we are happy for that."
The right-back also agreed with Ousmane Dembélé's comments, who was not happy after the final whistle with his team's attitude after going 2-0 ahead.
"I agree with Ousmane," said Hakimi.
"It's not possible to start the second half with two goals like that, a team that wants to win the Champions League can't do that. We have to take responsibility. We have to improve that, we'll talk about it after.
"We came with the intention of qualifying and we did it but we have to improve certain things and give continuity to what we do well."