The Dutchman netted spectacularly on his Old Trafford debut to get his side back into the match following Damien Duff's early opener for the visitors.
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"It was a fantastic finish from Van Persie, absolutely brilliant," he told Sky Sports.
"That typifies the goalscoring ability he has and it really lifted the place - we played very well from that moment.
"I'm pleased for both him and Kagawa. It's still early doors for them, Robin has not really played with the team much and this was his first real game and that will get better."
The Scot went on to lament the defensive mix-up between David de Gea and Nemaja Vidic which gave the Cottagers hope in the second half.
"It was a game we were dominating, playing brilliant football, recovering from a bad start and we talking about maybe scoring four, five or six goals," he added.
"But then we lost a stupid goal through bad defending and that made a real game of it."
Ferguson also praised goalscoring defender Rafael, adding: "Rafael has scored three or four in his time with us. He may not be prolific but he has the energy to do that - he played well."