Striker Sam Vokes opened the scoring for the Clarets in the 19th minute following good work from former West Ham winger Junior Stanislas.
Danny Ings then capitalised on a Danny Shittu error just before the hour to add a second while Liam Trotter had an effort cleared off the line for the Lions late on.
"The result didn't please me. We didn't do enough to get something out of the game. Burnley showed more hunger and desire for the game than we did and that's disappointing," said Jackett.
"We started the game poorly, on the wings they got in behind and got off crosses far too easily. The first goal is a prime example. He [Stanislas] went past two to deliver for Vokes to score.
"We didn't defend well, not with everything we've got, not for our life, which we do when we're playing well.
"Going forward, take the start of the second half, we spread the ball across the face of goal but didn't get on the end of it.
"We needed that goal to go and lift us and lift us again. We changed formation in the last half hour to free up the centre but we couldn't do enough.
"Burnley were in defensive mode by then, they had the lead and we couldn't move the ball well enough to get in behind them."