United scored second half goals through substitutes Marouane Fellaini and James Wilson while Falcao, controversially left out of the side that lost 1-0 at Southampton last weekend, was busy throughout but failed to get on the scoresheet.
"They were 90 very important minutes for me, I need to play and I'm very happy to be able to do so and obviously I'm very keen to be able to score again," Falcao said.
"I'm sure the chances will come as I had them today," added the Colombian, who will be hoping he impressed manager Louis van Gaal with his movements despite not finding the net.
Van Gaal left Falcao out of his squad last Sunday at Southampton where his team's 10-match unbeaten run was halted.
He then told the Colombian, who has managed three Premier League goals since his loan move, he must prove himself.
And while Falcao worked hard, it was Van Gaal's second-half substitutes who stole the limelight.
Young striker Wilson replaced injured centre back Jonny Evans while Fellaini, often criticised last season after a big-money mover from Everton, took Juan Mata's place at halftime as Van Gaal adopted a more attacking formation.
"It was a change to attack, and with a lot of risk," the Dutchman, who started with a 3-5-2 line-up, said.
United were indebted to goalkeeper David De Gea for keeping them in the game in the first half, especially with a brilliant save from a Charlie Austin volley after half an hour.
Van Gaal's adjustments early in the second half paid off with Fellaini heading home Antonio Valencia's cross two minutes after Green made a fine save from a header by Falcao.
Defender Marcos Rojo said United took more risks in the second half. "We knew the pitch was small and it would be a tight fight and we saw that in the first half," Rojo said.
"We were left with two centre backs but I think we controlled them quite well," he said of his second half partnership with Phil Jones.
(Editing by Martyn Herman)
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