Fellaini saved United's blushes against Young Boys on Tuesday night to secure a 1-0 win that propelled United into the Champions League round of 16 with a match to spare.
Early progress means Mourinho's men can increase their focus on turning around their poor league form, with Saturday's trip to embattled Southampton looking like the perfect opportunity to claw back the gap to the top four.
There will have to be a marked improvement on the way they played in the goalless draw with Crystal Palace, but Fellaini says the camp is in good spirits.
"I think the mood is good," Fellaini said. "The players are happy, but the most important thing now is to focus on Saturday and three points.
"It's always difficult to come back from the national team. Now we have a full week of training. All the players are ready to compete and start Saturday.
"Criticism is part of football, but we have to work. We are a team, we are together, and give everything too. Together we have to move forward and take the points."