United made progress to finish second in the Premier League behind champions Manchester City but Solskjaer said only by lifting the Europa League trophy on Wednesday will be able to brand the campaign a success.
"You go into every game as the next one is the most important one," Solskjaer told a news conference in Poland on Tuesday. "This now is a final that happens to be at the end of a season.
"You can define the season after tomorrow. So far we've improved but we'll only all go home happy if we win."
Victory would hand Solskjaer the first trophy of his reign at Old Trafford and United's first since the Europa League triumph in 2017 under Jose Mourinho. It has been eight years since United won the Premier League title, but Solskjaer is hoping lifting a trophy can act as a springboard.
"I think players, when they get the taste of success, when they win trophies, win something, it can go two ways; we've done it now and we can relax or, as I've had a few times, it just gives you more of that feeling." Solskjaer said. "You want more, you want it all the time, you want the feeling again with your teammates, with your club.
"This group of players has been working hard for a year, a year-and-a-half, together and it's the next step for them now to go and enjoy a game like this."
United head into the game as heavy favourites against a Villarreal side who finished seventh in La Liga. They have won just six of their last 12 games in all competitions under Unai Emery, who won the competition three times with Sevilla FC and reached the final with Arsenal in 2019.
Emery said that the side will try to make history as it hopes win its first ever European trophy.
"One of the aims of Villarreal was to break down barriers. We've broken the barrier of the semifinal in Europe and we feel proud of the work we have done," Emery said in a news conference. "We now have a responsibility to take a step forward. We need to enjoy this final and think about winning. We deserve to be in the final and to give our players the best tools possible to perform well in this final."
Emery, who defeated former club Arsenal in the semifinals, said he doesn't feel any pressure of eliminating another Premier League side.
"I feel a duty and obligation towards Villarreal. I want to defend this project and everyone that has worked throughout the years to build a big football project in a village. I have nothing to avenge. I'm very proud to have reached this final with Villarreal."
On the prospect of winning his fourth Europa League title in five finals, Emery wouldnt' compare any previous results to Wednesday's game.
"All finals are different. The past four finals I've been a part of, I've had some where my team was favourite but that was before the game. When the game starts, there are situations that can change the course of the game. We are eager, enthusiastic," he added.
Manchester United midfielder Bruno Fernandes said the match will be tighter than the bookmakers suggest.
"The team is getting better," Fernandes said. "Being in the final is good but to be perfect we have to win. The dressing room has confidence but it's 50/50 tomorrow. We have to do our best to go home happy."
Solskjaer also refused to rule out Harry Maguire while he continues his recovery from an ankle ligament injury, though the United captain was not able to train with the rest of the group on Tuesday.
ESPN correspondent Adriana Garcia contributed to this report.