Ralf Rangnick has told his Manchester United players he would prefer they solve disputes with him face-to-face rather than venting on social media.
Martial rejected Rangnick's claim that he had refused to travel ahead of the 2-2 draw with Aston Villa in January while Lingard disputed that he asked for time off last week, as had been suggested by the German interim coach.
"I never ever read or communicate by those social media accounts," Rangnick told a news conference on Monday ahead of the trip to Burnley.
"I don't exist there and wouldn't have time to do that so therefore it's always better and I always communicate with the players directly.
"I did that with Anthony Martial and Jesse but maybe I'm a different kind of generation. My generation didn't grow up with those kind of things.
"I can even remember a time when there were no mobile phones or internet so for me it's always better to communicate directly but again it's time now to look ahead.
"I know in both cases what I said to the players and what happened so for me there's no reason to discuss this anymore."
The 29-year-old is one of four senior players who will be out of contract at the end of the season along with Paul Pogba, Edinson Cavani and Juan Mata but Rangnick says he doesn't know if they will all leave the club in the summer.
"It's far too early to speak about that," he said. "It's also a question of what the players want and how does the club see it, but these are not any interesting topics or issues for us right now.
"For us right now it's to get the best out of the season and this is in the interests of the club, the fans, our current coaching staff but also the players.
"Even if they want to leave at the end of the season they have the chance to get a new offer from any other club, including Manchester United, and it is much bigger and much higher if they do well, play well and if we are being successful."