He felt they were the better side and recognises that Burnley, like Middlesbrough, will provide them with a tough game.
"I would have been disappointed with a draw at Middlesbrough because I thought we should have won the game," said Barmby.
"Obviously we ended up losing because of a wonder strike at the end, but the positives to come out of the game were that we restricted Middlesbrough to only one or two chances and that we made six or eight very good chances ourselves.
"We go to Burnley now and it will be a very tough game. It's one we're looking forward to and there's usually a good surface there. They've got some good players and will make it a difficult match."
Jason Tindall spoke on behalf of the Clarets today and it was always going to be the case that he was asked about the game at Hull five weeks ago when we came from two goals behind to win 3-2.
He said: "It was a very strange game. With 15 minutes to go we were dead and buried and were probably lucky to be only 2-0 down, but we got the first goal at a very important time and the second goal came just a couple of minutes after that.
"All of a sudden from Hull having the momentum it was quickly with us and Hull were on the back foot. Jay then popped up in the last minute to make it three goals in 12 minutes and when you look back it was a huge turning point for us.
"Off the back of four defeats before that and staring a fifth defeat in the face it was a great feeling for us and it's what kicked-started us off onto the good little run we are on now. What it did to was give us a great belief, to go to somewhere like Hull with their home record to come from 2-0 down and win the game 3-2.
"We have been very pleased with the form we have been showing recently and I would certainly say that the Hull victory was a massive turning point for us."
Tindall added: "Everyone says that football is a strange game. You know you win games you don't deserve to win and you will lose games you certainly don't deserve to lose.
"I think anybody who was at our game against Leeds at home will tell you that was a game we deserved to win and unfortunately we lost it. At Hull we didn't deserve to win the game but we did and that happened to be a big turn-around for us.
"It gave us a lot of confidence and we have taken that form on now and hopefully we can continue that."