The head coach claimed his side had a good first half before succumbing to ‘invincible’ Brighton in a poor second period.
Rangers have little to play for this season and it showed as some poor defending contributed to the thrashing at the hands of the promotion chasing Seagulls.
However, Hoops coach was impressed with an accomplished away performance before Anthony Knockaert’s stunning free-kick completely changed the tide of the game on the stroke of half time.
He said: “The first half was quite good. We got an unfortunate goal against us which they took really well but I didn’t think it was a free kick.
“Brighton capitalised on that well but then after they scored they felt invincible, they have that release of the first goal and then they can get into their stride and we could not get into ours.
“ We lost our way a bit and the second half was totally opposite to the first half.
“In that aspect, Brighton did very well but we already knew it was going to be a difficult evening.
“But before the first goal we were all right, we were pleased with how things were going and I felt we would get back into the game.
“It’s the second and third goal I’m disappointed about; we can defend that but they were better than us in the second half.”
Hasselbaink praised Brighton and wants his side to perform at their level with consistency to avoid another disappointing mid-table finish next season.
“They are a good side, Chris Hughton has done a magnificent job and it was difficult for us," he said.
“I am very disappointed because I don’t want to become a side of two halves, I want the first half and the second half to be consistent, it is important to be able to become a good and successful side.
“We have to concentrate on us and I want to finish our season on a high; today was a hard one to take, it was difficult but we have to take the pluses and learn from the minuses.”