Leicester’s 1-1 draw at Arsenal on Tuesday means if United, who travel to Aston Villa on Thursday, win their remaining five matches they are guaranteed a top-four finish.
They are in fifth place, four points behind Leicester with a game in hand.
Fifth spot could prove enough pending the outcome of Manchester City’s appeal against their two-year European ban.
“You never know what is going to happen, but the teams around us are playing well,” Solskjaer said at his pre-match press conference on Wednesday. “We just focus on this one, the next one.
“If we win every single one of them, we are in the top four. We cannot rely on help from anyone else, we just have to do it ourselves.”
The Norwegian boss said the team’s 16-game unbeaten run in all competitions had infused them with confidence.
“As a footballer you know you can’t just pick out your confidence from the fridge,” he said. “You have to (get) it from what you do every day in training, but the results, they matter.
“The last 16 games unbeaten gives us more confidence, but 16 games is nowhere near where a Manchester United team should strive towards. We can still go many games unbeaten if we concentrate on the right things.”
The form of Marcus Rashford, Anthony Martial and 18-year-old Mason Greenwood has dampened talk of the need for a new striker at the club after Romelu Lukaku left last year.
Solskjaer was asked whether he felt vindicated in the changes he had made.
“This isn’t a popularity contest, that’s for sure,” he said. “I have to make decisions that I think are for the benefit of the club.
“The decisions we made last summer and in January, bringing players in, allowing players to move on. I think, in my mind they were always for the good of the club and the team, both in terms of giving youngsters a chance but also in terms of giving trust to the other ones.”
He added: “So, for me, I would still make the same decisions if I could go back 12 months or six months.”