Lingard posted a video on his Snapchat account on Wednesday of him, team-mate Marcus Rashford and some friends in a hotel in Miami.
The England international was heard swearing and making crude comments which caused plenty of criticism from fans.
Former QPR manager Ian Holloway fumed at the 26-year-old, claiming he should be sold or sacked by United.
However, in response to Holloway, Durham says that is over the top and Lingard should not face any punishment.
Durham said Holloway’s claim that former Manchester United boss Sir Alex Ferguson had his players in check off the pitch was wrong and that they just got away with things because there was no social media back then.
The presenter says United should have a quiet word with Lingard but not take the issue any further.
“I don’t think it’s that offensive that people have to be serious offended by it,” Durham said.
“I cannot see a big, big problem here. Maybe somebody at United might just say ‘okay, make sure you know what you’re doing’, that kind of thing.
“But that’s the level, there should be no punishment.
“I’ve heard some people say he should be on the transfer list. What the hell’s that about?
“When I heard Ian Holloway talk about how Fergie ran a tight ship and all that – they weren’t all angels at Man United.
“And before that time, some players that we revere now, there was a massive drinking culture at Manchester United.
“But there was no social media then, there was no videos then.
“Otherwise these players, some of them, who knows, there could have been videos that led to the end of their careers, disgrace them, or might have got some help that they needed a little bit sooner.
“So there’s all sorts of things that went on back in the day that because there were no videos and you couldn’t take videos with phones back then, people got away with stuff.”