Wales were beaten 2-1 in Cardiff in the Nations League clash despite the hosts believing they had snatched a point when Rhys Norrington-Davies scored a last minute equaliser.
But Weghorst headed home the winner in the fourth minute of added time to put the Netherlands top of the group with two wins from two games.
The defeat leaves Wales bottom of the group despite Sunday's 1-0 win against Ukraine that saw them reach their first World Cup since 1958 when they head to Qatar in November.
After the final whistle in Wednesday night's game, Roberts confronted Weghorst following his heroics and appeared to ask him: "Why didn't you do that for Burnley?"
The clip clearly shows a frustrated Roberts approaching Weghorst before posing the question to the Dutchman.
But Weghorst hit back at his teammate with a few choice words of his own, appearing to tell Roberts "this isn't about Burnley, shut up."
It remains to be seen whether Roberts' remarks were said in a serious fashion but what is clear is that Weghorst didn't take too kindly to it.
Weghorst scored just twice in 20 appearances for the Clarets but has made it clear he has no plans to play in the Championship next season, something he fears could ruin his World Cup chances.
"We have clearly agreed in advance that I will not play in the Championship.
"The club would like to keep me and will do everything they can to return to the Premier League as soon as possible," he told Voetbal International.
"For next season it is important that I can perform at a high level, also with a view to the World Cup in Qatar. You shouldn't believe everything the media says.
"There is interest from Germany, England and Turkey. First I will focus on [the national team] and perform as well as possible, then we'll talk to Burnley about what's next."
Weghorst joined the Clarets in January in a £12million deal from German side Wolfsburg.
The manager at the time Sean Dyche swooped for the 29-year-old in the hope of avoiding the dreaded drop.
But things went from bad to worse culminating in Dyche being relieved of his duties and Burnley crashing out of the Premier League on the final day of the season.