The Red Devils had their first win at home after five attempts and Solskjaer seemed to be happy with the narrow victory despite admitting Manchester United were lucky.
The Norwegian tactician’s men were aided by a controversial penalty decision from referee David Coote as Bruno Fernandes stepped up to make it count for the hosts.
Speaking to the media after the game, Solskjaer reflected on his side’s crucial win over the Baggies.
“It's nice after the international break that you get a win. We needed that win at home. We looked unsettled towards the end even though we should score one or two more to have a more relaxed finish,” the former Cardiff City boss said.
“It's never comfortable against players of this quality. They had a couple of chances and David [de Gea] made two fantastic saves. Tight margins decide games but the mood is decided by the results.
"It's up to us to create momentum, we have the chance to continue the good start in the Champions League and Southampton away is a very difficult game as well. Hopefully we get a few more back and can kick on."
Fernandes’ penalty was retaken after Sam Johnstone was deemed to have come off his line.
Solskjaer added: "It's the same with David [de Gea] early on [in the season] when he made a save but he was an inch off the line. It's probably the beauty of Bruno's [Fernandes] style where the keeper goes a second too early. Sam [Johnstone] has developed into a fine keeper.
"The handball rule you can discuss over and over but we get into the box and the ball into feet so with VAR a touch can be enough and it's different to when I was playing when you had to be hacked down."
