Before his second-half goal, Cleverley had been sent through by Javier Hernandez when the contest was still goalless.
But amazingly, with only goalkeeper Rob Elliot to beat, Cleverley fired wide.
Although Anderson fired home an excellent 25-yard effort to put United ahead at the break, Rooney confirmed Ferguson was not happy.
"The manager wasn't too pleased with Tom because of that miss in the first half," said Rooney.
"But it was a nice goal by him and a great strike by Anderson.
"I am delighted for the two of them, especially Tom because it was his first one."