Louis van Gaal's team struggled to create chances yet again and needed an injury-time penalty from Rooney to avoid the embarrassment of a replay.
United fans again voiced their discontent at the quality of football on show, but the club's captain is adamant they are heading in the right direction.
He told BBC Sport:"You can go on and jump on everyone's bandwagon but we know we're improving as a team – we can feel that.
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"This cup can throw up a lot of surprise so it was just important that we got through and, thankfully, we've done that.
"I think it's always the case that as football players you want to win games and the way you win games is by creating chances and scoring goals," he added.
"We found it tough to break them down but we did what we needed to do, we won the game and we're in the next round."