The former LA Galaxy Designated Player was named in the starting XI as the Ligue 1 leaders twice came from behind against the Spanish giants, with Zlatan Ibrahimovic and Blaise Matuidi cancelling out goals from Lionel Messi and Xavi.
Barcelona has the advantage going into the second leg as a result of its two away goals, but the 37-year-old Beckham believes PSG can overcome the Catalans at Camp Nou.
"I think the draw was deserved," Beckham told ITV. "Obviously it was always going to be a game where they had a lot of possession, they have an amazing team and they played very well.
"In the first half, especially in the first 10 minutes, we had a few very good chances, if we'd have put one of those away then things might have been different, but then they got their goal. Then it was a real battle.
PSG looked destined to fall after Xavi's late penalty kick, but Matuidi's deflected equalizer at the death gave the club new life.
"It's better than it was at 2-1," Beckham said. "It's going to be difficult, but there's no reason we can't go there and get a result."
Beckham admited that he was delighted to be able to compete with the likes of Messi and Andres Iniesta, and he hopes to face them again, though the Argentine is a doubt after his substitution at halftime with a hamstring injury.
"I was obviously very happy to start. The manager has always shown a lot of confidence in me, especially in big moments. Tonight was a big moment for the club, and I was happy to start," Beckham said. "I hope he [Messi] is not injured, I hope he's fit for any game coming up, we wish him well."