Blaise Matuidi, who will miss next Wednesday's return leg after being booked, left the quarter-final tie in the balance when his last-gasp shot squirmed beyond Victor Valdes.
Barca had twice led, through Lionel Messi's wonderful opener and Xavi's late penalty, while Zlatan Ibrahimovic scored PSG's first equaliser, although replays showed he should have been flagged offside.
Beckham said: "In the first half, especially in the first 10 minutes, we had a few very good chances and if we'd have put one of those away it might have been different.
"Then obviously they got their goal, then it was an uphill battle, but I think we deserved the draw.
"It's better than it was at 2-1. We go there, it's going to be difficult but there's no reason we can't go there and get a result."
Barca lost Messi at half-time with a right hamstring injury, with reports suggesting he could be out for three weeks, and Beckham added: "I hope he's not injured, we all hope he's fit and ready to go for any game that's coming up. We wish him better."
Beckham was happy to be a part of such a big occasion once more, three years after he last featured in the competition while on loan at AC Milan.
"I was obviously very happy (to start)," he said. "The manager (Carlo Ancelotti) has always shown a lot of confidence in me, especially in big moments, and tonight was a big moment for the club and I was happy to start.
"I feel pretty much the same (as at Milan), it was only three years ago. I'm enjoying being part of these nights again, they're very special."
There has been much speculation this week over a potential extension to Beckham's short-term deal in Paris, which runs until the end of the season.
But he said: "Let's wait and see. Let's recover from this game and enjoy the rest of the season."