Veteran striker Nicky Forster, 36, condemned United to their third home defeat of the season with a two-goal lesson in how to finish.
Yet Abbott said: "We probably didn't do enough to win it. They came with a game plan and made life difficult for us.
"Credit to Brighton - they defended for their lives and did it very well.
"We didn't have the quality to break them down, but we should have had a blatant penalty in the first half when Danny Livesey was fouled.
"Everybody in the ground saw it but I don't blame the referee, it was just one that got away."