Albion and Palace drew 1-1 for the second time this season, courtesy of a late own goal by Joachim Andersen.
However, a draw was kind on the Eagles and the very least the hosts deserved after a dominant performance.
"It was a really difficult game," Gallagher, who is on loan from Chelsea, told Sky Sports.
"I don't think we played well.
"Second half was a little bit better but they [Brighton] were the better side, I thought, throughout the game.
"I feel we defended well but on the ball we weren't good enough at all."
Gallagher said he and his teammates showed a lack of confidence against a Brighton side which 'pressed well and made it hard for us'.
He added: "We just weren't confident enough to get on the ball and play, which we showed this season that we can do so that's a bit disappointing.
"They press high so we thought we would come a bit deeper and press their players high so we can go to the striker and play off there. It didn't really work, obviously.
"[The manager] said we needed to be better on the ball [at half time]. Obviously Jack [Butland] done well to keep us in the game was brilliant from him."
Gallagher has impressed for Patrick Vieira's side this season. Sky pundit and former Manchester United defender Gary Neville asked the midfielder, post-match, what he thought of comparisons to Chelsea legend Frank Lampard.
"I can't be compared to someone like that," Gallagher said. "I was happy to get a goal [but] I didn't think I played great."