After winning 12 of his 17 games in charge last season to guide United back into the Champions League after a two-year absence, Carrick was given a two-year contract.
However, as happened with Solskjaer five years ago, the new campaign has unravelled spectacularly and they are 13th in the Premier League, three points clear of bottom club Sunderland.
Although they recovered from their shock opening-day defeat to newly promoted Hull by coming from behind to beat Ipswich the following week, United have not won in the Premier League since. Their only other success in 11 games in all competitions came against Azerbaijan champions Sabah FK in the Champions League.
Their latest loss meant they have now gone seven games without a win, their worst run since they went eight without a victory under Louis van Gaal between 25 November and 28 December 2015.
Only Joshua Zirkzee’s injury-time consolation prevented United suffering their joint second-worst European defeat of all time.
The embarrassment was heightened by the knowledge that when they were last crowned European champions in 2008, Como were playing semi-professional football in front of a couple of hundred spectators in Serie D.
It is a basic reality that if Como’s star man Nico Paz, who opened the scoring after 118 seconds, created the second and added a third goal, said he wanted to leave Como, virtually every big club in Europe would want to sign him and United’s chances would be virtually non-existent.
They entertain 15th-placed Bournemouth in the Premier League on Sunday knowing that prior to last season’s amazing 4-4 draw, the Cherries recorded 3-0 wins on their previous two visits to Old Trafford.