Lingard, who joined the club at the age of seven, was denied a farewell appearance in United's final home game of the season against Brentford last week, which sparked a furious reaction from his brother Louie Scott.
In an emotional Instagram post, Scott branded United officials "lassless" while saying: "No wonder it's Conference League next year".
Yet Neville has fired back at the Lingard camp amid their complaints, highlighting the fact that United legends Bryan Robson and Steve Bruce also did not receive send-offs.
"There was a lot of nonsense spoken about Lingard," he said on The Gary Neville podcast.
"He's been at the club a long time and done a good job. But I've seen Bryan Robson and Steve Bruce not play in their last games for the club and not get a send-off in cup finals.
"They were both great captains and one of them probably is the greatest captain Manchester United have ever had.
"They didn't get the send-off they wanted so I'm not sure why Lingard deserved it.
"I was thrown away in West Brom in a toilet - sometimes it just doesn't work out, Jesse!
"To feel like you've a God-given right to get some minutes on the pitch based on how they played. Not one of them, other than David de Gea and Cristiano Ronaldo, can complain about what will happen to them this summer."
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