The club's board insists Cups should not be a priority.
But Taylor told the Evening Chronicle: "Obviously we aren't in Europe this year so we have to make sure we do well in the League Cup and the FA Cup.
"That's what we're trying to do. We must stand our ground in that. The last few seasons we have been a bit sloppy in certain games. We have to take the cups by the scruff of the neck and do well in them."
And when asked if United should play a strong team in the encounter with Man City, Taylor added: "Yeah absolutely. I'm sure that is what the manager will do.
"We want to do well in that. We talked about it at the start of the season and we want to do well in the cups."
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