Solskjaer's side breathed new life into their Barclays Premier League survival hopes with the triumph at Cardiff City Stadium, which moved them level on points with fourth-bottom West Brom.
Centre-back Steven Caulker grabbed two of Cardiff's goals, with the other coming courtesy of Sascha Riether putting through his own net for Fulham, who remain rooted to the foot of the table.
"Today was a big result for us. It was a big game for the two clubs and we got out on top," said Solskjaer.
"We've had many games that we have felt we deserved something from.
"But you can talk about that as long as you like. If you don't get results, it does something to the minds of the players."
Solskjaer was particularly pleased with the way his team responded to Fulham drawing level at 1-1 in the second half through Lewis Holtby.
"A win like today - especially the way we did it after coming to half-time with a lead, they score and you bounce back. That was a great feeling," added the Norwegian.
"They (Cardiff's players) never dropped their heads, they went forward again and started creating chances.
"You never know how human beings will react. You can prepare all you like, but they did it out there. (It was a) great response."
Cardiff now have 25 points and Solskjaer believes another 12 will be enough to secure safety.
"Yes, I think so. There's so many teams in and around us it might not have to be 37, but that's the aim. That's what we're looking at," he revealed.
"It (beating Fulham) means a lot to everyone at the club. It means a lot to me, the players, the fans.
"Everyone who cares for us really felt that's something we deserved, and of course it's great to get it in such an important game.
"It's a game that neither of us wanted to come off with less than three points.
"We can't relax, we've got to build on that."
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