Two goals from Steven Caulker and an own goal from Sascha Riether were enough to seal the points for the Welsh club, who are now four points above the rock-bottom Cottagers.
Lewis Holtby scored the visitors' only goal and for a short time the game was level at 1-1.
But, speaking to Sky Sports afterwards, Solskjaer said his team ran out deserved winners in the end.
He said: "If you could get a point for every goal you score as well then that would have been great.
"It was three important points and one we didn't want to lose so it's fair to say it was a big one.
"Confidence is not something you can pick up. It comes from the performances, results, and the belief is more important at this stage of the season. We deserved it."
Captain Caulker has been in impressive form for Solskjaer's men and the Norwegian was delighted for his skipper.
He added: "It's fantastic for Steven.
"Last week he could have scored as well. He's a defender but of course he's important for us and we have always been a threat at set pieces. The delivery was brilliant.
"We wanted to be in with a shout of wining the game after an hour. Our response to Holtby's equaliser was great but I expected it as well.
"My stamp will be on things the more that I am here. The lads are very professional, now it's about having more belief."