The 3-0 victory at Greenhous Meadow eased the pressure slightly on the Dutchman, but his future as United manager is still under huge threat, with Jose Mourinho widely rumoured to succeed him in the summer, per Samuel Luckhurst in the Manchester Evening News.
Van Gaal seemed in good spirits after the win at Shrewsbury, though, and he stayed behind to sign autographs, replying jovially to a fan who wished him luck for the rest of the season, per Sky Sports: "We'll need it, otherwise I'll be sacked."
See the full exchange below:
Monday's win saw United through to a last-eight home clash with West Ham United in the FA Cup.
Victory in the famous tournament—which United have not won since 2004—could be enough to save Van Gaal his job, but it seems unlikely.
The path currently looks set for Mourinho to take over, with Bleacher Report's Dean Jones insistent that the Potuguese could be a success at Old Trafford:
The only thing that might save Van Gaal is if he manages to secure qualification for next season's Champions League.
Failure to do so was what led to David Moyes losing his job in 2014, with the Scotsman being shown the door the moment a top-four Premier League finish became a mathematical impossibility after a defeat to Everton.
Will Van Gaal still be in charge at United at the start of next season?
United's hopes of a top-four finish this season are currently slim, as they lie six points back from Manchester City in the final Champions League spot with 12 games remaining.
However, that is not United's only route into Europe's premier club competition next term, they will also qualify if they win this season's Europa League.
After the first leg of their last-32 tie with Danish minnows FC Midtjylland, Van Gaal's side are 2-1 down on aggregate after a humiliating defeat in Herning last week.
Failure to turn the tie around when they meet for the second leg on Thursday will see Van Gaal's job hanging by a thread.
However, if they go on to qualify for the last eight and eventually win the competition—and perhaps also the FA Cup—the former Ajax and Barcelona boss may just survive for a little longer yet at United.