Pascal Gross had Brighton ahead on 70 minutes before Beto leveled seven minutes into injury-time.
"I felt as if we earned it, we deserved it," Moyes said afterwards. "I think every point in the league at the moment is so important to us. We don't want to lose games, we certainly don't want to lose with all the travelling supporters.
"The record we've had away from home we want to keep intact in some way. I think getting a point here today was a great result, even though last year we won here, but there's not many teams that come here and win, that's for sure.
"We were the better team in the second half, and really, the goal was disappointing because it looked as if we'd get knocked over, two or three different things didn't go right, didn't get it, didn't make it. Before you know it, we were a player down at the back and then he got in front of Jake (O'Brien).
"I wouldn't say (Brighton's goal) was totally against the run of play. I think whoever scored first was always going to have probably find the other team was going to come after them. We got after them a lot more after that and we put some more balls in the box and we looked a bit more threatening later on in the game.
"I say it all the time, (Beto's) a great boy and I'm really pleased with the way the supporters treated him today, because he's had it pretty tough and he's not scoring and finding himself out.
"But it was about this time last season when he started to score all the goals for us, so maybe he just gets that confidence now that gets him in and he gets the finishes."