Manchester United’s current malaise was laid bare as they struggled past third-tier Rochdale 5-3 on penalties after a 1-1 draw in the League Cup third round at Old Trafford on Wednesday.
Solskjaer made nine changes from the one that lost at West Ham United in the Premier League on Sunday, and laboured against their League One opponents before taking the lead through Mason Greenwood in the 68th minute.
Luke Matheson equalised eight minutes later, to send the tie into a shootout.
United prevailed, although, with keeper Sergio Romero making one save to spare their blushes as the hosts successfully converted all their spot-kicks and Daniel James slotted home the winner.
United struggled, but was not humiliated unlike West Ham United who were thrashed 4-0 at League One Oxford United.
Bournemouth was sent parking by third-tier opposition, losing 2-0 at Burton Albion.
Sheffield United joined the Premier League clubs to depart the competition as they lost 1-0 at home to Sunderland.
Liverpool won MK Dons to set up a clash with Arsenal while Chelsea pumped Grimsby Town 7-1 to give manager Frank Lampard a first home win since taking over in the summer.
Chelsea will face Manchester United in round four.