The pair started the game, with Wales looked like they had earned a point when Rhys Norpington-Davies headed an equaliser in the second minute of added time, following an opening goal from Teun Koopmeiners.
However, the Dutch went down the other end and Tyrell Malacia delivered a cross for Weghorst, who put the brakes on to create space and guided a header past Adam Davies.
At the final whistle, it appeared Weghorst refused to shake hands with Roberts, barging past him, and Roberts appeared to ask the £12m deadline day signing: “Why don’t you do that for Burnley?”
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Weghorst responded along the lines of: “This is nothing to do with Burnley, shut up.”
Weghorst scored twice in 20 games asthe Clarets were relegated from the Premier League, and he is set to leave the club, unwilling to play Championship football in a World Cup year, as he said to Voetbal International while on international duty: “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.
“For next season it is important that I can perform at a high level, also with a view to the World Cup in Qatar.”
Beşiktaş have offered a €100,000 loan fee and then €8m for the 29-year-old, with a salary of €2m a year, which has reportedly been accepted by Burnley and the player, who will now make the final decision on his next move.
Weghorst himself is believed to prefer a move back to Germany, or to stay in the Premier League, but would join Beşiktaş as a fall back option.
The forward was left out of the starting line-up for the final three games of the season, with Ashley Barnes preferred up front alongside Maxwel Cornet.