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The pair were doing post-match interviews pitchside after the disappointing 0-0 draw with Scotland at Wembley, where some Scots had remained.
The Tartan Army were chanting loudly as expected and decided to give both Rice and Mings some stick as they gave their thoughts on the stalemate.
In a video doing the rounds, Mings was subjected to chants of, "You're just a sh*te Grant Hanley!" from the raucous Scottish fans.
The Aston Villa man cracked a smile but his teammate Rice didn't appear to take it so well when the supporters turned their attention to him and shouted, "You're just a sh*te Billy Gilmour!"
Chelsea prospect Gilmour was named Man of the Match after delivering a composed midfield display in his first ever start for Scotland.
England's best chance of the drab display fell to John Stones early on the first half, with the Manchester City defender heading against the post after producing an insane leap from a Mason Mount corner.
Harry Kane was also on post-match duty but his interview with ITV was drowned out by a chorus of boos from angry England fans in the stands.
The England skipper and talisman was barely involved in the game and ended up being replaced by Marcus Rashford after 74 minutes.
But despite Kane looking a little out of sorts and to manage a shot on target, Three Lions' legend Alan Shearer believes he will still lead the line in the final group game against Czech Republic on Tuesday.
'There's no doubt about it: Harry Kane will and should start the next game," Shearer told the BBC, per Metro.
"Forget about leaving your captain and your leader out. We know what he can do, we know what a good player he is. One chance and it's in the back of the net."
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