The Northern Ireland international broke his leg in the first half of the 4-0 Premier League defeat and whilst there is no timescale on his return, he faces a lengthy rehabilitation period.
Dallas spent Saturday night at Leeds General Infirmary before travelling to London for surgery and further tests.
The 31-year-old was Leeds's player of the season as they finished ninth in the 2020-21 Premier League and has been influential again this. He had been the Whites' only league ever-present in an injury-ravaged season where his versatility was essential, filling gaps across the defence and midfield with high-quality performances.
Since the summer of 2019, the only league match he has not started for Leeds was at Blackburn Rovers in July 2020.
He has been as influential under Jesse Marsch as he was under Marcelo Bielsa, with the American making him part of his seven-strong "leadership council" of senior players.
Marsch spoke about his importance before the game.
"Stuart has been fantastic," he said. "His mentality, his work-rate and his ability to understand what the games require at such a high level.
"I know that left-back (where he has made many of his appearances for the American) is not his preferred position or his best position.
"I haven't had chances to see Stuart in the six (holding midfield position). His national team coach was here a couple of weeks ago, and he said that he is used more as a wing-back, in a three.
"His intelligence and his flexibility are an incredible strength."