Southampton executive chairman Nicola Cortese's decision to sack Nigel Adkins back in January also came under fire, and Neville believes that the Blues' win after their disappointing FA Cup defeat to Wigan Athletic last week shows that sticking with a manager is sometimes the best course of action.
"If anything demonstrates the importance of stability, of consistency, of not making rash decisions, then Everton's performance did," Neville wrote in his column in the Daily Mail.
"After they had been knocked out of the FA Cup by Wigan last weekend, many people might not have been expecting their 2-0 win against Manchester City, a performance that was already superb even before they went down to 10 men with 30 minutes to go.
"But you know what you will get from David Moyes and his Everton players, and that performance epitomised their character. In a 30-year marriage you might get the odd bad day, but you don't throw away what you've built up over time because of that."
The win took Everton three points clear of local rivals Liverpool in the Premier League.