Lasse Schone struck a 74th-minute equaliser, cancelling out Edinson Cavani's first-half goal as Ajax earned a point in the UEFA Champions League clash in Amsterdam.
De Boer was pleased with his team's approach in the second half on Wednesday, and said it was exactly what they needed to produce against top-quality opposition.
"I'm happy with the second half. I even felt at the end we could have won the game," De Boer said.
"The second half we showed we can definitely play football but of course things can get better.
"The positive is that I could see the players come out of their shells, which is exactly what was needed against this type of opponent."
Cavani's scrappy goal put PSG ahead in the 14th minute, before Schone's fine free-kick from the edge of the area saw Ajax clinch a point.
De Boer praised goalkeeper Jasper Cillessen and defender Joel Veltman for their performances.
"I have to give my goalkeeper Jasper Cillessen a lot of praise for denying them a second goal," he said.
"I was pleased with Joel Veltman, who was on Zlatan Ibrahimovic and prevented PSG from passing the ball to him.
"However, we cannot make mistakes at this level and we have to cut those out."
