United ended a dispiriting run of four consecutive home draws in the Premier League by beating Tottenham Hotspur 1-0 on Sunday courtesy of a 29th-minute goal from the resurgent Henrikh Mkhitaryan.
Fellaini, who had conceded a late penalty to allow Everton to snatch a 1-1 draw at Goodison Park a week earlier, was booed as he prepared to come on as a stoppage-time substitute, but Mourinho played it down.
"I had that feeling (that Fellaini got booed)," he said.
"I accept it because from the fans you have to accept everything, and especially fans that are giving so much to us without getting so much from us.
"The only things they are getting from us are honesty, professionalism, dedication, but they are not getting the results they expect from us.
"They are so supportive of us. They can also be a bit critical. They have in their mind the mistake that Marouane did at Everton and no more than that.
"He's a player and a person I like and the person is even more important than the player. So he will have always my protection and my trust."
Mkhitaryan struck after Ander Herrera intercepted a pass by Spurs striker Harry Kane and threaded the ball forward, the Armenian driving into the box and powering a shot past Hugo Lloris.
Mkhitaryan was stretchered off in the 84th minute after being caught by Danny Rose and rolling his left ankle, but Mourinho played down the injury, saying the 27-year-old would be out for "maximum two weeks".
United remain sixth, 13 points below leaders Chelsea and six points off a Champions League berth, but Mourinho is hopeful his team can start to reel in the sides above them.
"We still have our ambitions this year and obviously to win this match puts us in a position where we can feel them (the teams above)," he said.
"We can be in touch with fifth, with fourth. We can feel them with so many matches to go, so we can say this result was very important for that.
"We were six points from Tottenham. We lose today and six goes to nine. And nine is more difficult than three. So the result was important."
Kane lost the ball in the build-up to Mkhitaryan's goal as Spurs tried to build play up from the back.
Centre-backs Toby Alderweireld and Jan Vertonghen had moved towards the touchlines to provide passing options, which left Herrera with a gaping boulevard down which to pass the ball to Mkhitaryan.
But Spurs manager Mauricio Pochettino said: "That is how we want to play. We built a perfect action from the back. When that situation happens, it's football and we need to be clever enough to try to react.
"Our offensive players can make a mistake. We need to understand that they need to take a risk. Then we have a lack of reaction in that situation when we lose the ball and we allow them to score.
"We try to play under our philosophy and we try to create a chance."
Ten points below Chelsea, Tottenham's hopes of replicating last season's title challenge are beginning to fade, but Pochettino says his team have plenty of time to claw back the deficit.
"The concern is not too much," said the Argentine, who revealed midfielder Mousa Dembele would undergo tests after taking a kick to the foot.
"The Premier League is tough. Chelsea started the season very bad and for different circumstances they changed the system and look how they are now. There is too much time to recover and reduce the gap.
"We are in a good position and it is a long way to the end of the season."