Michael Carrick's early opener gave the Reds an ideal start at a windswept Britannia Stadium, before Robin van Persie's second half penalty sealed a win which brought the Premier League title three points closer.
"It's difficult coming here and the conditions today were dreadful, really," Rooney told MUTV. "It was probably the most wind I've played in, so we had to deal with it, be disciplined and give a good performance. We did that and thankfully we got the three points.
"It [the derby] was horrible really. No matter how many points clear we were, it was a derby game we wanted to win and unfortunately we didn't do that, so the next best thing to do was show we could respond to that, come to Stoke and get three points."