The Clarets approached Thursday night's penultimate game of the season at Aston Villa sat in the Premier League drop zone but pushed Leeds back into the bottom three on goal difference by sealing a 1-1 draw.
Burnley's goal difference is 20 goals better than United's meaning that their destiny is in their own hands ahead of Sunday's final day when the Clarets host Newcastle United and Leeds visit Brentford.
Leeds will be relegated with Burnley surviving if the Clarets beat the Magpies or match United's result against the Bees but Jackson said he could not agree with suggestions that his side had achieved their mission through their point at Villa Park.
"I wouldn't say it's mission accomplished," said Jackson to BBC Sport.
"We knew that the least that we wanted to come away from here with was a point.
"There's a bit of disappointment that we didn't get the three that we would have got if we didn't give that goal away early in the second half.
"But everything that I have seen tonight is what this group does.
"They've had to really dig in, they've had to work, the work they've had to put in there was terrific so we are going to need that again on Sunday.
"We can't hide that it's in our hands but we know there's still 90-plus minutes of hard work and emotion and everything that has got to go through on that day.
"But it's just about us now and resting up and making sure that we are prepared to go for Sunday."