The Mexican striker persevered after a string of missed chances against the resolute visitors, before nodding home Antonio Valencia's 84th-minute cross to see off David Moyes' side.
Chicharito told MUTV: "There was a little bit of frustration, but you need to keep going in the next play, and the next, and the next, because you can't stay there only thinking 'I missed it', you need to be ready for the next one. Thankfully the goal came and near the last minute.
"For 90 minutes we kept going and kept going because we wanted the goal, wanted the three points as soon as possible. We keep going, keep working and it was a difficult day also because it was hotter and that made us a little bit more tired. But the history of Manchester United is like this - we can score in the first minute and also the last minute."
The victory over Everton precedes a run of games in which the Reds contest a two-legged Champions League final as well as facing the rest of the Premier League's top three, but Chicharito confirmed that United only had eyes for seeing off the Merseysiders.
"It's the only thing we have in our mind and thankfully we got it (the win)," he said. "It's unbelievable because we know the importance of these three points because we need to get all the points we possibly can because we can win the league. This is the key part of the season, we have Schalke then the two games against Arsenal and Chelsea.
"It's very important. Here the thing always in our mind is that we have to win, we need that