Burnley boss Vincent Kompany called it "ridiculous" and "bizarre", while the club's co-owner said it was "truly disgraceful".
The Premier League might be enjoying a staggered winter break but controversy involving the video assistant referee (VAR) flared in the first of this weekend's five games.
With Burnley on the brink of a crucial 1-0 win in a game of huge significance at the bottom of the table, Luton's controversial 92nd-minute equaliser - a header by substitute Carlton Morris - was allowed to stand.
There was a lengthy check by the VAR after Elijah Adebayo appeared to impede keeper James Trafford as Morris scored.