A deflected stoppage-time goal from Blaise Matuidi, whose earlier booking meant he will be suspended for next week's return leg, left the quarter-final tie in the balance.
"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," Beckham told ITV1.
"Then obviously they got their goal, then it was an uphill battle, but I think we deserved the draw tonight.
"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 Lionel Messi at half-time with a right hamstring injury 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."