Amid fierce speculation over Mourinho's future, United fell two goals behind inside 10 minutes on Saturday – the first time in Premier League history that has happened at Old Trafford.
Fellaini, who came on at half-time in place of Scott McTominay, told BT Sport: "The manager asked us to be men and to not be afraid and just play.
"That's what we did. The first half was a difficult moment for us, but we were more aggressive in the second half and we played more direct and created more chances."
Mata, meanwhile, feels positive results can fix any crisis in football, even a story that has generated the level of debate as Mourinho's United future.
"We needed something like that," he said. "It was very difficult to come back but we created more chances than we scored.
"We gave everything we had to win and in the second half we felt we had nothing to lose, and it is natural to create more when that happens.
"It is a relief and we feel that we got what we needed. In football, results fix everything. In the second half we tried especially for the fans, and tonight they go home happy."