Cardiff ended a four-match winless run with a 1-0 triumph at St Mary's Stadium last weekend, a result that moved the Welsh side to within three points of safety.
A crucial home Premier League fixture against Stoke City takes place on Saturday and Solskjaer says his players will go into it in a buoyant frame of mind.
"Results change moods in football. Last weekend did just that," Solskjaer said on Friday.
"We need to build on the momentum that win (gave us).
"There's a lot of belief in there now that we can get the job done over the next four games.
"We've got to reach our top form. We're at home and it's a chance to build on our momentum gained from our win last weekend."
Solskjaer knows it will not be easy, though, as Stoke head to Wales in great form.
Stoke beat Newcastle United 1-0 last week to keep up a great run under Mark Hughes and sit inside the Premier League's top half.
"We play a team that are in top form," he added.
"They've won five in seven and are safe this season. They'll play with a freedom and confidence."
Cardiff goalkeeper David Marshall has urged his side to win two league games in a row for the first time this season.
Of Cardiff's six other Premier League triumphs, none have been followed with a win, with five being defeats.
"We've not had back-to-back wins all season. That's something we want and need to do to put us in a good position," Marshall said.
"It was a perfect weekend last weekend. It gave us belief we perhaps didn't have after the result with (Crystal) Palace (a 3-0 home defeat)."
"Back-to-back wins are now the aim. We need to come out of the traps quick but Stoke are in good form and will be tough.
"We needed a perfect weekend last time out and got it. We're more than confident that we can get the job done (and stay up) with four games left."
