The Red Devils needed penalties to see off their League One opponent after it ended 1-1 in regulation time.
Mason Greenwood’s opener was cancelled out by a 76th-minute equaliser from 16-year-old Luke Matheson.
While Solskjaer was relieved with the victory, he admitted a few big changes are required at the club, to ensure it gets back on track.
“As you normally are when it gets tight, you’re happy when you win, you’re through and you learn again about different things.
“That’s our tradition, to do it the hard way. The crowd was fantastic tonight so of course, we just have to take one game at a time but also we’ve got more than one eye on the future.
“We know we have to change things throughout the club and we are doing that,” Solskjaer told Sky Sports post-match.
