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 said. "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."
United now need a maximum of seven points from six remaining games to clinch a record-extending 20th league title, and Rooney is determined to garner a further three at Upton Park next week.
"It's a tough game on Wednesday, West Ham away, and it's a massive game now," he said. "We'll go there and try and get the three points. Hopefully we can do that and then move on to the next one.
"We're in a great position and I'm sure every United fan and player would have taken this position before the season started. We just have to make sure we move on and push ourselves over that line."
Wayne was speaking to MUTV and Sky Sports.