Van Gaal had endured a barrage of abuse from unhappy fans during last Saturday's 0-0 draw against West Ham, but that was nothing compared to the insults thrown at him after United suffered an embarrassing Champions League exit on Tuesday.
With a host of former United stars including Paul Scholes and Roy Keane queueing up to question van Gaal following that 3-2 defeat at Wolfsburg, the pressure is mounting as the Dutchman takes his spluttering side to Bournemouth on Saturday.
United are without a win in their last four matches in all competitions and reports claim van Gaal has lost the support of sections of his squad, with some players said to have been amazed by his decision to replace Juan Mata with the inexperienced Nick Powell against Wolfsburg.
But Fellaini is adamant van Gaal retains the full backing of the dressing room and, with fourth placed United only three points behind leaders Leicester, the Belgium international expects a strong push to win the title.
“We trust him,” Fellaini told NBC Sports. “He is the manager, it is his philosophy and we have to continue like that.
“I am sure the goals will come and the chances as well. Yes, of course (we can win the title). At the moment we are in the top four, we are there.
“It is a tough month but we have to continue like this. We know at Manchester United the expectations are high.”
United could be facing fourth bottom Bournemouth at the worst possible time as Eddie Howe's team will be buoyant after their surprise win at Chelsea last weekend.
That loss threatened to bring the curtain down on Jose Mourinho's second spell at Chelsea after a traumatic season at the Stamford Bridge.
But Mourinho's players, regularly reported to be disenchanted with their manager this term, responded to claims that the Portuguese coach was on the verge of the sack by beating Porto 2-0 on Wednesday to book their place in the Champions League last 16.
That victory appears to have bought Mourinho breathing space as he tries to lift Chelsea, currently only two points above the relegation zone, back into contention for a top four finish.
Mourinho still has no margin for error with Chelsea's next assignment a tricky trip to Leicester and he could do with misfiring striker Diego Costa following up his vote of confidence with a lengthy scoring spree.
“Despite things not going well he is not to blame,” said Costa, who was recalled by Mourinho against Porto after a spell on the bench.
“When four or five players are not playing well it is more difficult. The manager has been fighting and encouraging us to turn this around.”
Leicester's remarkable rise to the top of the table in their first season under former Chelsea boss Claudio Ranieri makes them dangerous opponents for the west Londoners.
But Ranieri fears Chelsea are coming back into form just in time for Monday's trip to the King Power Stadium.
“Their record does not mean anything as Chelsea are Chelsea and Mourinho is Mourinho,” Ranieri said.
“I'm sure at the end of the season they will be in the top four.
“I respect them a lot because I watched the Porto match. They played very well with good concentration.”
Arsenal also reached the Champions League last 16 in midweek thanks to Olivier Giroud's hat-trick in a 3-0 win at Olympiakos.
Arsene Wenger's side, two points behind Leicester in second place, return to domestic action at bottom of the table Aston Villa on Sunday and winger Theo Walcott says their spirited success in front of a hostile crowd in Greece bodes well for their title challenge.
“We never give up and you should have seen them buzzing right at the end in the dressing room,” Walcott said.
“That is the spirit we want in this team. It is the spirit that we can push on and improve.”
Third placed Manchester City host managerless Swansea, who sacked Garry Monk in midweek.
Bournemouth v Manchester United, Crystal Palace v Southampton, Manchester City v Swansea, Norwich v Everton, Sunderland v Watford, West Ham v Stoke
Aston Villa v Arsenal, Liverpool v West Brom, Tottenham v Newcastle
Leicester v Chelsea
Original source: Van Gaal will win title - Fellaini