Substitute Mustapha Carayol scored twice in the final six minutes for the visitors, who by contrast are now unbeaten in their last five Sky Bet Championship games.
But Thompson insists the Seasiders' slide down the table, after a fantastic start to the campaign, is cause for concern.
"The players are working hard but we're lacking quality in the final third," said Thompson.
"We told the lads before the game and at half-time that we needed to watch the counter-attack and we've been done twice, which is frustrating.
"We felt we were starting to get on top of the game and we got hit by a sucker punch. It's worrying the results we're having at the moment and we don't want to be looking over our shoulders over the next few weeks."
Thompson also claims that the club are powerless to stop star midfielder Tom Ince, linked with a move to Swansea, leaving the club if the right offer comes in.
"Tom is a fantastic asset for us at the moment and the last thing we want is to lose him," he added.
"Obviously if someone comes in and offers a lot of money then there's not a great deal we can do about it, but we don't want him to go.
"We need good players to kick-start our season again. We haven't discussed anything regarding him leaving and potentially any money coming in."
Boro goalkeeper Shay Given was tested by Ricardo Fuller and Ince either side of the break, before Carayol's double sealed the points for the visitors.
The winger cut in from the right on 84 minutes before bending a fine effort into the bottom right-hand corner and then, in added time, he fired into the top left-hand corner.
"It was very good result and performance," said Boro boss Aitor Karanka. "It was a tough first half, we didn't play in the first half, but in the second period the subs worked well and we got the result.
"Everybody knows Mustapha is a quality player and he needed that for his confidence. He took both goals very well and I'm very happy for him.
"I said when I first came here when we lost two or three games, my philosophy is always thinking about the next game.
"We were three points away from the relegation places and now we're not far from the play-offs - but my mentality is the same."