The Norwegian was speaking in the immediate aftermath of United’s heartbreaking Europa League Final defeat at the hands of Villarreal.
The Red Devils went into the game as overwhelming favourites against a side that finished seventh in La Liga.
However, after being held 1-1 during regular and extra-time, the Spaniards ran out 11-10 winners in a marathon shootout for the ages.
The defeat means Solskjaer’s wait for a trophy goes on after failing in the latter stages yet again.
But in an open post-match assessment, he claimed United need as many as three players to help turn their fortunes around.
“I’ve been delighted with the effort, the desire, the determination of all of the players, I can’t fault them at all,” Solskjaer said. “We’ve probably done as well as anyone could imagine.
“We are here now, we need to do better, we need to work better, work harder, cleverer.
“But as I said, two or three players to strengthen the starting XI and the squad all together is important for us to go even further.
“Because I’m sure our contenders or challengers will also want to improve and we want to improve as much as we can.”
Solskjaer’s public demand is sure to put pressure on the Glazer family after another month of controversy for the controversial owners.
The likes of Erling Haaland, Jadon Sancho and Declan Rice are on the Old Trafford wishlist, meaning the Americans will need to hand the manager a huge warchest.
Co-owner Joel Glazer broke the family’s silence earlier this month following the huge backlash to the European Super League.
In which, he boldly suggested that they are still ready to back Solskjaer by bringing in “top-quality recruits”.
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“Our top priority is, and will always be, competing for the most important trophies, playing entertaining football with a team comprised of top-quality recruits and some of the world’s best homegrown talent.
“Under Ole, we feel we are absolutely on the right track,” the statement read.
“Success on the field must be underpinned by solid foundations off it. We have supported sustained investment in the team over many years, and that will continue this summer.”
Unlike his predecessor Jose Mourinho, Solskjaer made it abundantly clear that finishing as runners-up in the Premier League wasn’t acceptable and that improvements must be made in order to win silverware.
“The boys have been really, really good but just came up short tonight, unfortunately. That’s penalties, we could have been sitting here saying a successful season after the same game.
“But trophies matter and that’s what matters at this club.”