United are at the Emirates today.
Neville told the Daily Mail: "Whatever has happened, there has always been a huge level of respect between the two clubs.
"There is an acceptance and understanding at United that Arsenal do things the right way. They play the right way, have a great stadium and great traditions. You have to respect that.
"They're coming in for criticism at the moment, as is Arsene Wenger, but I do believe they are very close to winning a trophy.
"It is a fine line between success and failure and the Carling Cup final defeat this year was a big moment for them.
"They have the right manager and the right principles. They could do with more experience but I think Wenger himself has said that they need to show a level of maturity but that doesn't come easily.
"We had those lessons as young players, losing to Monaco in the Champions League, losing to Barnsley in the FA Cup and losing the championship in the last week of the season at West Ham.
"Disappointments are part of what makes a football career and having those bad months in March and April, when it all falls apart and you get knocked out of two or three competitions in the space of two or three weeks, are part of the learning curve.
"These Arsenal players will grow in experience. For people to question Wenger and suggest it is time for him to go is ridiculous. They couldn't have a better manager than him. And we need more teams like Arsenal in the Premier League."