Inigo Calderon's first-half strike was enough to settle it in favour of the Seagulls, with some Blackpool fans venting their frustration at boss Paul Ince during the game.
"We're obviously disappointed to lose in the manner we did," said Rae.
"It was really only one incident in the first half, we've switched off and allowed the boy to run and he's beaten the keeper at the near post.
"Apart from that I don't think there was a great deal between the two teams.
"We huffed and puffed and tried to get some momentum going. We need the fans to get behind us and all be in it together.
"I've been a fan myself, and I know they are disappointed. The problem from our point of view is we haven't got a lot of options to change things. We can understand the fans' frustration."
Rae also confirmed the Seasiders would be in the market for a striker in January.
He added: "We don't have a great deal of options up front.
"Without a doubt January is something we need to address. We don't have a great deal of resources. We don't have the option of changing players like Brighton did."
Brighton's victory, their first at Bloomfield Road since September 2000, moves Oscar Garcia's side three points clear of Blackpool as they close in on a top-six berth.
The visitors dominated the first half and it eventually paid off when Calderon was allowed to cut inside and, with space opening up before him, beat Matt Gilks with a low, left-footed effort despite the keeper getting a hand to it.
Blackpool showed a renewed vigour early in the second half, with Dan Gosling seeing a low shot blocked but Garcia was delighted with the victory.
"I'm very happy with the performance of all the players," said Garcia, who confirmed Will Buckley had picked up a hamstring injury.
"I'm very happy also with Inigo Calderon. He wasn't playing for a long time but he's always prepared and always focused.
"He was outstanding here and in all the training sessions. He deserved the goal and I'm very happy for him. He plays with a lot of enthusiasm.
"I think most of our performances have been good and I am happy with the performance of the players. We are always looking forward and hoping to play attractive football for the fans, which I have said from the day I came here.
"I'm very happy, we have great travelling support and for us it's very important to see a lot of Albion fans coming here to see this game. This victory is for them."