United's 2-1 loss to Leicester City on Tuesday saw City clinch the title with three games remaining in the season.
And if the Red Devils want to challenge their neighbours next season, Solskjaer says they must be active in the transfer market.
"If you want to take up the challenge with them 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."