"It's always good to start a match," he told RMC. "It was a pleasure. I feel at home, I'm playing with super players in a super team. I felt good, but I cannot always play 85 minutes immediately."
Beckham was harshly booked shortly before being substituted after a confrontation with Jordan Ayew, but he insists such incidents are par for the course in big games.
"The coming together with Jordan Ayew? This happens in big matches like this. The tension is high. I'm not complaining," he said.
Sporting director Leonardo added that Beckham's display was evidence that the former Real Madrid star has not simply been signed for commercial reasons.
"He did not arrive just so we could take pictures, press conferences and sell jerseys. Today was the confirmation of that," he said.
Coach Carlo Ancelotti also praised Beckham's contribution in his post-match press conference, but revealed his frustration at Uefa's decision to hit Zlatan Ibrahimovic with a two-game Champions League ban following his red card against Valencia.
"Beckham had a very good game," said Ancelotti. "As usual, he delivered good passes, and played well in the axis with [Blaise] Matuidi. He showed he could play, even though he is 37.
"It was a different game to last Sunday. Marseille used different tactics. They played deeper to prevent us from playing. In fact, it was easier for us to keep the ball.
"Ibrahimovic's Champions League suspension? I was surprised when he got the red card. To see Uefa impose a two game ban is incredible. I hope they will reconsider their decision."