Following their impressive derby win over Tottenham last week, Mikel Arteta's side were fortunate to come away from the Amex Stadium with a point.
Brighton dominated the majority of the match but lacked the cutting edge in attack.
Arsenal remain unbeaten in four consecutive Premier League matches and move up to ninth place in the table.
"I don't think we deserved to win the game, we have to take the draw with the performance we had today and improve," Arteta told the BBC.
"We didn't make enough right decisions, every time there was a duel where we could escape pressure and attack open spaces we came up short and against this structure we had to do better.
"We have conceded one goal in the last five games which is really positive ... we can now focus on the things we are doing well and work on the ones we need to improve."
Brighton were unaffected by the soaking conditions and managed to dominate and control the game throughout the first half.
Shane Duffy also had an opportunity moments later but his header went past the post.
Arsenal's evening was compounded when Bukayo Saka limped off with an injury late on.
"It was a difficult game, they made it hard and we have to give credit to them," Ramsdale said.
"We have got to get around that, we have to show more composure and intensity on the ball and make it harder for them."