Mexican international Javier Hernandez equalised for the Hammers after Glenn Murray's opening goal for Brighton, but the Seagulls went on to seal the win through strikes from Jose Izquierdo and Pascal Gross.
Full-back Cresswell has said that he is frustrated with the result, which left West Ham three points outside the relegation zone.
"We came here hoping to get something and I don't think we were good over the whole 90 minutes," the Englishman told the club's official website. "We had a couple of spells in the game in the first half where we could have got something.
"But [Izquierdo] put one in the top corner in the second half and to be fair to him, it's a great finish, but we didn't react well to that. We didn't look like scoring in the second half.
"We had a bad start but we had spells in the first half where we did well and had a few chances. We didn't get the rub of the green though and second half we didn't react to the set-backs we suffered."
West Ham's next game is against Watford in the Premier League on Saturday.