Goals from Jackson and Scott Wagstaff secured a 2-1 win over Blackpool - the Addicks' first home win on a Saturday afternoon this season.
Charlton have now picked up back-to-back league victories, having beaten Watford 4-3 on New Year's Day, to edge further away from the relegation zone.
In between came a disappointing home defeat by Huddersfield in the FA Cup, but Jackson insists the confidence is coming back to the side which ran away with the League One title last season.
"I saw that stat in the week, actually," said the midfielder. "We hadn't won at home at 3 o'clock on a Saturday, so it was nice to put that one right.
"The home form hasn't been terrific and we aim to put it right in the new year. Obviously we got beaten in the cup but it's two wins in the league and one at home so we are pleased.
"We want to keep winning games, that's two on the bounce and we can go to Blackburn next week with confidence. We want to put a run of wins together, get to the safety mark, whatever that will be, and see where we go from there."