Van Persie was booed by the Gunners faithful as he returned to his old stomping ground at the weekend, having left for Manchester United last summer.
He has enjoyed a superb season to help United win the Premier League title and scored from the penalty spot in a 1-1 draw on Sunday, but Evra thinks the Dutchman was stung by the criticism he received and should have been shown more respect.
"People forget what he achieved for Arsenal," Evra said. "But he showed them that he hasn't made the wrong choice.
"It was a long time that he didn't win the league at Arsenal, but he has come to Manchester United and done it.
"He did a good job for Arsenal and I was really disappointed for him [with the negative reception]. I think he felt it as well.
"To take that penalty, he showed what a world-class, top player he is. He kept his nerves down to score and I am happy for him."
United had already been confirmed as champions before the clash with Arsenal but were still determined to win the game, and Evra insists they will play with the same intensity for the remainder of the season.
He explained: "A lot of people expected to see Manchester United not playing well because we have already won the title. That is not the mentality of this club.
"It is important for us to win every game. It was a big game for us and people might laugh when I say that, but that is the Manchester United culture. It will never change."
Evra admits he was surprised, and impressed, by the way Arsenal played after years of being criticised for their lack of physicality.
He said: "They were one of the most aggressive teams I have played against, but it was good to see Arsenal like that.
"They get abuse, with people saying they are a team with good footballers but they are not aggressive enough. They certainly were against us."