The Merseyside club's main forward Rooney failed to convert two notable chances during the game and so did United's Lukaku.
Lukaku first set up Henrikh Mkhitaryan for their second goal, then scored from close range himself, before Anthony Martial wrapped things up by scoring a penalty in stoppage time.
The Spaniard finished with three saves on the day en route to keeping a fourth clean sheet in five Premier League games.
Neville, though, believes that United's favourable fixture list has helped them to this position, with there still plenty that two sides setting their sights on the crown have to prove before silverware is handed out. They have more obligation than us. I think City clearly have an fantastic squad, and when they play at their very best, they produce a level of football few can get close to.
The 31-year-old was greeted warmly by the home fans as he played his first game against the club since returning to Everton in July.More news: Memory sale leaves a hollowed-out Toshiba
However, Jose Mourinho - famed for an incredible home record throughout his managerial career - has returned the Theatre of Dreams to it's formidable status as one of the toughest away days in the country.
After the game, Koeman was clearly annoyed at "The Special Ones" comments about his team saying "I read the United programme and my colleague told me about Everton spending £140m and so they need to go for the top four". Ander Herrera was player of the season and is not starting matches.
And Herrera feels that City's transfer dealings make them favourites for the title, and as such, he believes the pressure is on them, rather than United. I will try to enjoy every minute I have on the pitch.
But manager Jose Mourinho has said the nature of the injury would not be known until after the results of the scans.