Javier Hernandez's goal kept United six points ahead of Chelsea and nine above Arsenal, who have a game in hand.
"Games are running out for our rivals and we're up for it," said Ferguson.
"I enjoy this critical stage of a season when we are involved in big games that come thick and fast and I think we will be OK."
United now have four games remaining in the league and are closing in on a title that would take them above Liverpool's tally of 18.
They face Arsenal at the Emirates on Sunday, 1 May and entertain Chelsea at Old Trafford a week later, with Ferguson urging his players to wrap up the title by beating both of their nearest challengers.
"The thing that puzzles me is they [the media] keep saying Arsenal and Chelsea have got to play us still, like we're going to lose to them," added Ferguson. "But why shouldn't we win those games?
Phelan admits Man Utd selection was a risk
"As I said to the players, forget all that nonsense. Just try to win your games and you'll be all right, keep your heads and don't get carried away."
Manchester United left it until the 83rd minute to end the resistance of a dogged Everton side, Mexican Hernandez heading home an Antonio Valencia cross at the far post.
It was the striker's 19th goal of his debut season in England and Ferguson has admitted he did not expect Hernandez to get off to such an impressive start after his £6m move from Chivas.
"Javier has done better than everyone expected," added Ferguson. "We thought that because it was his first year, he would just get used to the English game and get strengthened up.
"He has passed all those tests. He is first in at nine o'clock every morning and he is the last to leave. He is a truly dedicated boy."
Hernandez says he would swap all of his 19 goals for a Premier League title.
"Of course it's a dream come true, this season," he said. "If we win the Premier League, that's an unbelievable thing. If I could swap all the goals for us to win the league then I would do it.
"We know we are almost there, but we can't afford to think like we've already won it. We go day by day, week by week.
"I'm very happy, but I'm happier because we got the three points. Here at Manchester United we need to win every game and it doesn't matter who scores."
Moyes praises Everton defence in defeat
Everton boss David Moyes paid tribute to his side and was left to rue their lack of an attacking threat, with United keeper Edwin van der Sar only having to make one save of note.
"It's disappointing to lose it late on because we'd been so resilient for so long and kept Man Utd at bay with some outstanding defending and goalkeeping," said Moyes.
"I can't fault players for their performance, but we didn't play well enough going forward and didn't cause them enough problems.
"We've got a few out injured and we're not quite where we'd like to be but the results in recent weeks have been terrific. Today they stuck at it and for most of the game they kept United at bay.
"I think our players should be at the top end of this league, they deserve to be. They competed really well."
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