United restart their European campaign against Austrian side LASK on Wednesday (05.08.20), holding a 5-0 advantage from the first leg back in March, and feels that winning the competition could be the launchpad for a period of trophy success for the Premier League club.
The Norwegian coach said: "When I won my first trophy as a player it made me more hungry.
"The team has developed through the season and we are delighted at finishing third in the Premier League. If we can get our hands on a trophy it's a big step forward."
Solskjaer's side enjoyed a strong run of form in the second half of the Premier League season to qualify for the Champions League and he suggested his players are keen to end the prolonged campaign with silverware. United will progress to the quarter-finals should they complete the victory, with the closing stages of the delayed tournament being played in Germany.
The 47-year-old manager, who is yet to win a trophy as Manchester United boss, explained: "They want to play, they don't want the break, they're bothering me all the time."
The Red Devils scored four second-half goals to register a 5-0 victory in Austria, although Solskjaer felt the margin of victory flattered his team.
He said: "We were winning 2-0 after 60 minutes and scored three in the closing stages, so we know we have to perform.
"There's opportunities for players to stake a claim, if they get through."