The England midfielder missed a gilt-edged chance in the first half but atoned for his error in the second period by curling beyond Rob Elliot to net his first goal for the club.
And Rooney disclosed post-game that the Red Devils squad, and Cleverley in particular, were subject to some harsh words at half-time prior to running out 2-1 victors.
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The 26-year-old also expressed his delight at returning to the starting line-up following a lengthy lay-off with a thigh gash, sustained against Fulham.
He added: "Of course it is good to be back. It's been just over four weeks now since I last played so I'm delighted to get out on the pitch playing and it was a good run-out for me.
"I'm obviously delighted and hopefully there are a lot more games to come. I feel good but obviously it is always difficult on your first game back after a few weeks but it was great to get the minutes under my belt and hopefully that will benefit me."
Rooney's sentiments were echoed by midfielder Darren Fletcher, who returned to captain United after recovering from a debilitating bowel problem.
"It's great to be back," the Scot enthused. "I've had a few reserve games and a run-out in the Champions League last week and it has been a long time coming so it is just good to be back, especially at Old Trafford and in a winning team."