Boro took the lad with their first attack after six minutes, when Kris Boyd tapped home after poor defending, and Scott McDonald doubled the advantage after 23 minutes.
"We started sloppily, it was a sloppy 25 minutes and we were punished for it. But you cannot afford to start a game like that and expect to come away with anything," said Baraclough.
"We had to start at the tempo that we had finished against Hull. We didn't and were punished for it. We were playing against quality players, a £20million team.
"I've been involved in a lot of teams where if they go 2-0 down after 20 minutes they pack up. I've got a young group here and they got themselves together, all credit to the players because they created chances.
"The home results aren't good. The more you get beat at home the more people will look at it. But you can't tell me the players have played badly from start to finish. I don't think they have done. We just missed chances, we had double the chances they did."
Tony Mowbray, the Middlesbrough boss, told his players they stlll had a lot to prove despite claiming their first away win of the season.
"I have been in the Championship before and you can see how difficult it is in every game," he said.
"We will go to Swansea on Sunday and see how good we are. Nobody is getting carried away outside of our dressing room.
"We're still looking over our shoulder and below us. First we need to get into the pack and once we do that we can have a look at how consistent we need to be to get in the play-offs."