United managed to get a win very late on against Wolves, thanks to a strike from Marcus Rashford that was deflected into the back of the net by Romain Saiss in the 94th minute.
However, whilst United have been propelled into second in the Premier League, the Norwegian has refused to state that they are in a title race.
Speaking after the game, Solskjaer stated that "There's no title race after 15 games."
"You can lose the chance of being in a race in the first 10 games, of course you can."
"But play another 15, get to 30 and then maybe we can start talking about a title race, when you get to March or April, when we have at least played more than half a season."
However, he is confident that United will try their hardest to stay near the top, saying that "the belief is there", adding that "Of course the players go into every game thinking we can win against anyone anywhere."
"Away we've shown what we're capable of. I think we're improving at home as well and this result is massive for confidence and for the attitude."
United were not at their best against Wolves, but it may be expected with a team that did not feature several regular starters such as Fred, Scott McTominay, Victor Lindelof and Anthony Martial.
Solskjaer was still proud of his team's performance on Tuesday, especially with their desire "to create that little bit of luck" and end the year on a very positive note.
Speaking on the squad's improving mentality, he said that the desire the squad has, was obtained "by personalities, by recruitment".
"Of course we've added that spark I think but also when you get results, and things are going your way, that helps."
"We brought it up early on in pre-season that we need to add more points towards the end of games. That's something we do as a club - we've done that so many times and we've done that quite a few times this season as well."
"Physically we last games more. I have to say I feel a bit for Wolverhampton, they have had one recovery day, which I don't think is right for any player or any team to only have one day between games."
This result is part of a fantastic turnaround for the club's season, managing to go nine Premier League games unbeaten.
United have been criticised for their home record so far this season, but they are seemingly starting to shift their fortunes, getting eight points from their last four Premier League home games.
The Red Devils will be welcoming Aston Villa on New Year's Day, a crucial game that United have to win in order to keep the pace with Liverpool and the rest that are chasing the Premier League title.