The Red Devils are currently enjoying an impressive pre-season campaign, having won all their five games played so far.
And to hit the ground running in the upcoming season, Solskjaer has urged his side not to be deceived by the results of their pre-season exercise.
“We've been very pleased with it. It's been nice seeing the boys come back to pre-season in good shape," he told talkSPORT on Thursday.
"But then again, no points have been handed out, and it doesn't really matter when Chelsea come to Old Trafford on 11th August.
"We need to improve and we need to be better. The more we improve and the more we get better, the bigger the chance we can challenge for trophies at the end of the season.
"These boys have shown their capabilities. If we just stay level-headed, I can see us improving a lot.”
Following Jose Mourinho’s departure, Solskjaer took charge at the helm in December, turning things around but won just two in his last nine games after he was contracted permanently as the side finished sixth on the league log.
The Norwegian trainer believes his side will improve in the 2019/20 season, stressing the change of manager last season took its toll on his players.
"Football is an emotional game. It's always difficult when a new manager has to come in and the previous one loses his job, but the players handled it well over the summer and they've come back really fit and sharp," he said.
"I know how fine the margins are in football and how easily things can go from good to bad. It's a mental game, it's all in the head.
"We didn't handle the ups and the downs well enough, we know that. That would be down to mental tiredness because it was a draining season for everyone, but we'll be better this year."
