Fellaini, who made a £27.5 million transfer deadline day move to Old Trafford, made his United debut in the Red Devils' 2-0 win over newly-promoted Crystal Palace on Saturday, coming off the bench for the last 30 minutes.
And the 25-year-old midfielder impressed during his cameo appearance, going close to opening his account for David Moyes' side only to be denied a dream start by Julian Speroni, who thwarted away Fellaini's 25-yard half-volley.
But despite catching the eye on his United bow, Fellaini has admitted that he has struggled to adjust to the fast-paced training at Manchester United, and that the step up in quality has come as a shock to the system.
In an interview with the Metro, Fellaini revealed: "I have a problem with the intensity of the training because I am playing with big players.
"It is quicker than at Everton. But I am happy. I like the game and I like to play.
"The quality is better than Everton but Everton are a great club as well."
Many outsiders have suggested that Manchester United paid over the odds for Fellaini, with his £27 million plus price tag coming into question from some quarters.
Moyes could have signed the Belgian international for £4 million less had he bid for the former Standard Liege midfielder before his buyout clause expired on July 31, but Fellaini is ignoring all the talk and remains fully focussed on helping the team.
"The price is not my problem. £25 million or £30 million or £20 million – whether you are expensive or not, players are just players.
"I want to play midfield defensive and if I can help the team further forward then good."
Fellaini will be looking to make his full debut for Manchester United tomorrow night, as Moyes' men play host to Bayer Leverkusen in the Champions League at Old Trafford, kick-off 19:45.