It means Burnley are now just one point behind 17th-placed Everton and – despite playing a game more – the Merseyside strugglers have a very difficult looking run-in on paper.
On the game
Jackson was delighted with the application of the Burnley players and he highlighted the collective efforts of everyone at the club.
"It was a terrific effort from everyone involved," he said. "We started well, had a good intensity and we spoke about bringing the crowd with us."
"Physically I thought we won a lot of duels and were competitive all over the pitch. That is nothing knew and they have that in them."
Given the quick turnaround for Burnley, it would seem like Jackson will remain in caretaker charge for Sunday's match against Wolverhampton Wanderers.
"I will probably speak to the chairman later in terms of whether he wants us to prepare the team on Sunday. That is the way we are moving with this now. Just enjoy the night and tomorrow we can think about Wolves.
"It gives the group belief. I believe they can [get out of this]. Sometimes the group need to perform like that and remember what they are."
Everton now remain just a point away from Burnley – just like they were after the two clashed at Turf Moor a fortnight ago – but Jackson doesn't want his focus to be on other teams.
"I am just looking at the next thing this group needs to do and the performance levels they need to hit again.
"I don’t really want to speak about Everton and I don’t think it is right to speak about other teams, I think you should just deal with your own business. Don’t worry about anybody else.
On Roberts over Lowton
Jackson decided to bring goal-scoring Roberts back into the team after the Welshman had been dropped for two matches. He felt that Matt Lowton was still working hard to gain fitness.
"There was a little bit of fatigue in Lowts at West Ham. He has missed quite a few games and has not played so it is just about getting him up to speed a bit more. I didn’t think he did anything wrong the other day but there was a game today and there is another one on Sunday."
The stand-in boss was able to provide some clarity on the injury that Ashley Westwood had sustained and admitted that his situation had given added motivation to his team-mates on the field.
"It is a fracture and a dislocation. The operation went really well and we said before the game about turning his tele on and giving him something to smile about so hopefully we have."
On the job
Since stepping in from his position with the club's under-23s, Jackson has orchestrated a mini-revival of form and he seems to have the backing of the players. But he didn't want to be drawn on his own future following the game.
"I've not spoken to the chairman, I've not had chance to speak to anybody! He asked us to prepare for the game, if he asks us again for Sunday, we’ll do it, that’s where we are at.
"I've got no meetings planned. We're in for a recovery day and work day for the lads who haven't played.
"If we're asked to prepare again for Wolves, we will do, we’ve thought ahead a bit to Sunday, but we're just happy to help the club and help the players perform.
Asked about how he would feel taking the role until the end of the campaign, he added: "At the moment we are looking ahead to the next game if we are still here.
"There is a lot of good people around here and you can’t do this on your own, it is impossible. A hell of a lot of work goes into it from the staff to everyone involved in the club."