Liverpool were crowned English champions for the first time in 30 years without kicking a ball on Thursday when Chelsea beat Manchester City at Stamford Bridge.
Liverpool’s 19th title triumph, which sparked wild celebrations around their Anfield home ground, left them one behind United’s record haul.
“First of all, any team that wins the championship and a Premier League deserves it and they deserve credit,” United boss Solskjaer, who won six league titles as a player at Old Trafford, told reporters.
“It’s a hard league to win, so well done to Jurgen (Klopp) and his players.
“For me, every time you see anyone else lift the trophy it hurts. I reckon that’s the feeling everyone associated with Man United – all players, staff and supporters. Of course we want to get back to winning ways and that’s our challenge.”
Solskjaer is hoping FA Cup glory can be a springboard for further success, with United heading to Norwich on Saturday in the quarter-finals.
United are fifth in the Premier League, still in the race for a Champions League spot, and are well-placed to reach the last eight of the Europa League.
“I think first of all the FA Cup is a fantastic tournament, and a fantastic final to play a part in, a fantastic trophy to lift,” said Solskjaer.
“For our team, it’s a new team and to get hands on a first trophy and win a first title would be fantastic and hopefully a catalyst for more things to come.”
Solskjaer plans to rotate his squad at Carrow Road, where Jesse Lingard will feature, having yet to play a minute since the restart.
“Jesse has come back after the lockdown with a smile on his face, loads of energy,” he said.
“Unfortunately, last week he fell ill for a couple of days but we’ve done all the tests and he’s fine, so he’ll be involved against Norwich now and hopefully he can kick on.”