Everton produced their biggest win in 23 years against United, with McCarthy opening the scoring after just five minutes with only his third goal for the club.
And McCarthy said that while Everton had endured a disappointing campaign so far, they are now looking to end their season on a high after winning five of their last six matches in the Premier League.
“Obviously it has been a frustrating campaign,” he said. “We have picked up a few wins on the bounce and now we want to kick on and finish the season on a high.
“But we won’t get too carried away, it is a big win against Man United, we will take it one game at a time now and try and go unbeaten until the end of the season.
“It is not usual for me to get in those positions and it is good to get a goal, but the most important thing was to get the three points today and I thought all the lads were magnificent.
“We knew Man United were going to come at us and we hit them on the break a couple of times and scored goals from it, but I think from start to finish we were magnificent all over the pitch and it is a big three points. We want to finish as high in the table as we can, we take it a game at a time now and look forward to next week.”
Meanwhile, Everton centre-back John Stones said he was relieved to have finally scored his first goal for the club, with the 20-year-old doubling the Toffees’ advantage with a header 10 minutes before half-time.
“It has been a long time and I have had a lot of pressure off players and staff saying I need to get more goals,” said Stones. “It is a special feeling for me and to keep a clean sheet and score three against Man United, it is a big day for us and keeps us on a run now.
“The big games are the ones you always look forward to, the big players bring the best out in you and I definitely enjoyed myself today, as I am sure James did as well – he covered every blade of grass – and it a credit to the team.
“I think we all know we have been under par this season and we have definitely showed in the last 10-15 games that we are coming back to ourselves and to go on this run is going to do us the world of good going into next season.”