United needed a late winner from Javier Hernandez to settle yesterday's crucial clash.
"I could feel the goal coming," Sir Alex told MUTV. "We had the momentum and the crowd was up. When the crowd gets going, it sucks the ball in.
"Today's game was tricky. Everton are very resilient and some of their defending was fantastic today. Their goalkeeper and two centre-backs were absolutely brilliant. We had shots blocked near the line, some misses and the goalkeeper made two or three great saves.
"Our decision making wasn't up to scratch in the first half, when we had some great openings, and we could have had the game finished by half-time. But in the time-honoured fashion of Manchester United, we don't do that. We wait to the very end. It keeps everyone hanging and on the edge of their seat, but we get there.
"You say to yourself, 'It's going to be another late one here.' You can just smell the history of the club and so it was to be.
"The important thing is we never gave up. We took gambles, we took risks. We put Wayne Rooney in the middle of the pitch, we brought Ryan Giggs on, Michael Owen on. Jonny Evans has not had many games, neither has Fabio, but they both saw it through and showed great resilience and determination to get through it.
"It was a fantastic performance by the lads in the way they kept going against a good Everton team. I think we can be very pleased today. We've got the result we want."