After a first-half that had seen Jordan Rhodes put Aitor Karanka's men in front, and Jamie Mackie reply for the home side, it was the promotion chasers that edged clear as Gaston Ramirez and Ben Gibson both scored before the hour-mark, meaning that Tjaronn Cherry's late goal was nothing more than a consolation.
And it was the nature of the two Boro goals at the start of the second-half - both coming from Grant Leadbitter corners - that frustrated Hasselbaink.
"The most disappointing thing was conceding from two set pieces. We need to defend those better, but the reaction was important. It was good to see the spirit we showed," he told Get West London.
While the Rangers boss will be disappointed with the result, and the nature of the goals, he can take plenty of positives from the way his side performed against one of the favourites to go up to the Premier League.
And the scoreline could have actually been better for the home side as Sebastian Poulter had an effort controversially ruled out with just under 20 minutes to go, as the linesman incorrectly flagged for a goal-kick in the build-up when in actual fact, Junior Hoilett had managed to keep the ball in.
Nevertheless, the defeat arguably ended any slim hope Hasselbaink's men had of sneaking into the play-off places so he will be keen to ensure that their defensive work is much more solid next season to allow them to go after a top six spot.