But he was left frustrated by the officials after a number of decisions went against the Clarets in the second half as they earned a 1-1 draw at Aston Villa.
Burnley knew four points from their last two games would be enough to stave off the drop, and the point at Villa Park saw them leapfrog Leeds, meaning they have to match or better the Whites’ result on Sunday to retain their Premier League status.
Ashley Barnes – who Villa felt should have been dismissed for a stray arm that connected with Tyrone Mings – gave the Clarets the lead from a penaty right on half-time, after Maxwel Cornet was brought down by Emi Buendia.
Buendia equalised shortly after the interval, with the goal allowed to stand despite Matty Cash taking a throw in with one foot well within the playing surface – before a VAR check for a spot kick for handball against Lucas Digne went against Burnley.
Then substitute Matt Lowton was harshy dismissed late on as his follow through connected with Calum Chambers’ foot in a challenge.
Jackson said: "First and foremost, what the group went through, the spirit and fight they put into that was amazing.
"I thought it wasn't a silky match in terms of us, but we did what we needed to do, and I think if we hadn't conceded early in the second half we would have frustrated them more.
"But that was the least we wanted to come away with from here, a point, so we're pleased with that."
It was Barnes’ first Premier League goal since Febtruary 2021, on his 450th career appearance, and Jackson added: "He did (nerves of steel), we spoke this morning about making sure we know who the penalty taker was, because bodies are coming in and out, so we’re glad we did that because Barnesy kept his cool.”
Asked whether he was lucky not to be sent off, Jackson admitted: "I don't know, I know the way Barnesy plays, I know the way Mings plays, they are two big guys going at it, I haven't seen it back, so I don't know.”
But on the officials, he mused: "People have commented on it (the foul throw) and I've seen a little clip, it doesn't surprise me, to be honest, I think there's a handball as well, very similar to ours the other day, but we know what happened with that and we have to make sure now that we just take good positives out of that tonight.
"It's been a real shift of hard work and the other side of football.
"I don't know what you can say, people can say that's because you're not a big side and they are a big side, but why not just referee the games properly and fairly for both teams?
"That's all anyone wants to see, that's just commonsense, to be honest.”
And on Lowton’s red card, Jackson will assess the video before deciding whether to appeal: "The lad's disappointed, I don't think there's any malice in it, he's come on late in the game, the emotion, the adrenaline is pumping, he knows we're trying to get this point, and he's just overrun it.
"You could see if he didn't time it right, it could look a bad one, but I don't think there was any malice in it.
"I'll have to look at it.”