United’s defeat to Leicester on Tuesday confirmed their rivals’ latest Premier League crown, their third in four seasons under Pep Guardiola.
Solskjaer made 10 changes to his side for the visit of Leicester in an attempt to deal with an intense fixture schedule of four matches in eight days.
He handed Premier League debuts to teenagers Anthony Elanga and Amad Diallo but it was not enough to overcome Brendan Rodgers’ side, with Bruno Fernandes and Paul Pogba starting on the bench and captain Harry Maguire out injured.
“If you want to take up the challenge with [City] we need to strengthen our squad,” Solskjaer told BT Sport. “Congratulations to them. They have had a fantastic season.
“I am very pleased with my boys that have made it to the last 10 days with a Manchester City side ahead of us that are lauded as the best in Europe.
“We want to take the next step and it might be that we need a couple more to strengthen the squad.”
United have been linked with forwards Erling Haaland, Harry Kane and Jadon Sancho ahead of the summer transfer window.
Rivals City have invested heavily in developing perhaps the deepest squad in Europe under Guardiola in recent seasons, which has allowed them to compete on multiple fronts and reach their first Champions League final.
“They’re where we want to be. They’ve put the bar where it is,” Solskjaer added. “It’s up for us to take the next step.”