Solskjaer's men claimed a 1-0 triumph at St Mary's Stadium on Saturday, a result that came just a week after a 3-0 hammering at the hands of relegation rivals Crystal Palace.
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But Cardiff finally gave their fans something to cheer about on the pitch, with Juan Cala's 65th-minute strike giving them all three points for the first time in six games.
Solskjaer's side are still three points adrift of safety with four games to play, but the Norwegian retains the belief that Cardiff can stay up.
"What happened galvanised the squad," Solskjaer told Wales Online. "I may have to make the players mad about something because the focus we had against Southampton was exactly what we need every week.
"They concentrate on football - and I deal with any issues which come up. This is still not in our hands, but if we do our job then, with a little help, we have a chance.
"This result has given everybody a massive lift in terms of belief, but we still need help from other matches.
"When it comes to off-field issues we deal with those as a club and move on. It's important players focus on what they have to do, while the fans keep believing and stay behind us.
"After the final whistle at Southampton when other results were announced people realised we are in with a shout.
"Not many people expected us to take three points against a very good Southampton team, a very good club.
"It's a result that really galvanises everyone. We were really hurt by the performance we gave the fans and ourselves last week, but the team spirit has been fantastic leading up to the game.
"This is a start for us and we hope it ends in a miracle. It'll take performances just like today; it's exactly what we need."