Solskjaer had previously criticised his players' poor start against Burnley last week which saw them trailing 2-0 though they eventually managing to come away with a point.
Rashford scored the only goal of the game after nine minutes.
A huge trio of fixtures against Paris Saint-Germain, Chelsea and then Liverpool follows after the Fulham game, and United could go into that as a top-four team should they win and Chelsea lose to Manchester City a day later.
"We didn't string passes together, we didn't control the game as much as I liked". We can find the gaps in between the defenders and the gaps between the lines, that's something we're really working on, because we don't want to be a predictable team.
Solskjaer also added that the only negative about his new role is missing his family who remain in Norway: "It's been fantastic so far".
And it seems that Molde are more than happy to let Solskjaer flourish at United, after the manager revealed that his old club - or his parent club, if you like - told him not to come back when he was first offered the chance to take the reins at Old Trafford.
MMA fighter wanted on murder charges captured
KCEN reported that in a court document before she was murdered , Scott called Marks "a pathological liar" and "a psychopath". Marks and Pease have a child together and Pease, who is from Washington state, had accused Marks of domestic violence.
Loaned by Norwegian club Molde until the end of the season, Solskjaer is making an ever-more compelling case to be made permanent manager, given results and the obvious easy rapport he has with supporters and players.
"Both owners wished me all the best because they knew this is something I dreamed about".
He continued on Pogba, "I think he can look back on these games and say that he is on his way".
Rashford can make himself Manchester United's centre-forward - they don't need to go and buy anyone else, he's your centre-forward that can take you to a title or a Champions League. I feel very good at the moment, I feel in form, I can run a lot and recover the ball and I feel good when I have it on my feet.
The interim boss said: "I enjoyed Marcus' finish". "I will always advise the club, especially if they ask me".