The veteran manager believes his side played well on the night, but didn't do enough to create any clear cut chances, and praised Fellaini's match winning performance
The long-serving Red Devils coach praised his side's display despite failing to cope with the huge presence of Marouane Fellaini, who's header in the second half won the game for the Toffees.
Van Persie made a late substitute appearance in his debut for the club, but failed to register a shot on target, as the visitors found it difficult to break down a hardworking and resolute Everton side.
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"With Robin in your team you know you want to use his ability against centre-backs in situations he is very good at - but we didn't use him enough."
Ferguson had to deploy a make-shift defence with Michael Carrick at centre-back and Antonio Valencia at right-back, with Phil Jones, Chris Smalling, Rio Ferdinand and Jonny Evans all injured, but refused to criticise the backline despite struggling to cope with Fellaini.
"He [Fellaini] is a handful: he is a big, tall, gangly lad and they just lumped the ball forward to him, that's all they did," added Ferguson.
"They worked from that base all the time and they got a goal from him, so it's justified.
"Centre-back is a problem but we coped quite well, I don't think you can criticise their performance in that respect.
"It was just difficult to handle him when they were knocking these balls up to him.
"Michael did fine, good on the ball and applied himself well, they all applied themselves well."
Sir Alex was also keen to praise goalkeeper David de Gea, who was in superb form in the first half and had made several key saves which kept the Red Devils in the game going into the break, and also stated that his team were the better side.
"We were the better football team, they had eight shots on target and De Gea did very well for us in that way," he told MUTV.
"But we had the possession and made some great openings without actually finishing it. That was the only difference. These shots on targets the goalkeeper did really well.
"Other than that we played good football, good combination play, on another day we would have won the match."