The only goal of the game came eight minutes from half time but Jackett felt there was nothing between the sides before the interval and felt his side should have had a penalty in the second half as well as questioning the disallowing of a goal.
He said: "The first half was fairly even, but we gave away a poor goal and that was very disappointing. We did enough and showed a lot of spirit.
"We are still missing that little bit of luck. I felt we should have had a penalty, John (Marquis) has worked himself into a good position and the defender's stuck out a leg, but the ref's not given it. We need that bit of fortune for a decision to go our way."
He added: "I think we did everything but score in the second half. We had a disallowed goal, a penalty appeal and those things just happen like that when you are down on your luck.
It could be that we have to get someone in now. I don't think it's any secret that we just haven't scored enough goals this season and that is something we will try to address. We've got a couple of weeks now because of the international break and I'll have a look at it again.
"Confidence is low in the dressing room - the players are obviously disappointed and one win in 10 games is obviously not good enough."
Eddie Howe was full of praise for his players after they worked so hard to hold on to the lead in what was not the most fluent of performances in the heat at the Den.
"The main thing today was the determination and desire to grind out a win," a delighted Howe said. "That pleased me more than anything. We are a really small group, but the spirit is as good as I have known it since I have been here. It's getting better all the time and that was the key to the win."
He came onto the pitch at the end with all his backroom team for a huddle in front of the Burnley fans and said: "The huddle at the end was a result of that spirit. We did it regularly at Bournemouth because we had great success there for quite a while, so hopefully you will see more of it!"
He saw the Clarets win the game with an adaptation of the corner routine that won us the game at Hull last season and also got us the first goal in the 3-1 home win against Middlesbrough in April. He said: "The corner routine worked and I'm pleased with it because when there are such fine margins between winning and losing, you can win a game on a set-piece and so it proved.
"It was a battle and I don't think either side really got going. Technically it wasn't the best match, but I think we showed a different side to us, especially second half.
"We hadn't really seen that quality of determination and putting bodies on the line and I thought we defended very well and our goalkeeper was magnificent.
"He saved us when we couldn't clear the danger. I was a bit worried late on when they had a penalty appeal late on.
"Initially I thought it was a penalty, but speaking to David (Edgar) he said it was a dive and the lad (Marquis) has admitted it, so we are pleased that went in our favour because it's ended with our first clean sheet in a long time and that is the most pleasing thing today.
"The stats are often talked about and you can use them to prove whatever you want, but the clean sheet had been around our neck all season and we were desperate to end it.
"It's a tough ground and it's always difficult here. The crowd get behind them and I thought we withstood the pressure very well.
"That's two away wins now. We are certainly moving in the right direction as a side and the more we play together, the better we'll be.
"It's been a good couple of weeks with the Carling Cup win as well. We are progressing after a tough run of fixtures. Forest gave us a huge confidence boost and we go into the international break in good spirits now. We have a game in hand on most sides, so things look a lot more positive than two weeks ago."