The Reds go into their final Premier League of the season in third place in the table - but they are still not certain of their position in the Champions League.
Looking ahead to their final game, Solskjaer - whose side need a point against Leicester to make sure of Champions League football next season - said: "Let's get this game out of the way and get third position and continue the growth and the journey this team's on.
"Of course we've had some hard times this season, some setbacks, but I think we've shown and we've proved that this is a team going places.
"If we get a result against Leicester, I think everyone will say that this journey has been a good one. But then again, this is not the end of the journey. If you get there, it's not 'breath and relax', it's 'go again'.
"We know there are two teams too far ahead of us, so we have to step it up even more."
The Premier League season restarted without fans, and Solskjaer thinks they've been a big miss for his team.
He said: "I think the players have just got used to this situation and we've just got to get on with it. The fans would have made a big difference, of course they would have, at both home and away games.
"Football without the fans, for me, is not the same. They're a part of football because we are together and it should be with the fans."