Atkinson failed to send off David Luiz for a high tackle on Marouane Fellaini five minutes before half-time, electing to only book the Brazil international instead.
Luiz arrived second to a loose ball and made enough contact with Fellaini’s thigh to leave his opponent requiring lengthy treatment from United's medical staff.
Graeme Souness, while analysing the game for Sky Sports, accused Atkinson of ‘bottling’ the decision and claimed it was a certain red card offence.
“That's not a difficult decision to make,” he said. “If you look at where the referee is. He's getting a full view of it. Does he not see six studs showing there? Does he not see that? He says ‘I've seen something, so I'm going to give him a yellow card.’
“By the shape of David Luiz going for the ball, that is extremely high, showing six studs... it's a red card. Martin Atkinson has completely bottled it.”
Keith Hackett, the former head of the Professional Game Match Officials Limited, has also criticised Atkinson’s decision, claiming he “lacked the courage” to dismiss Luiz.
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Hackett does, however, believe that the error can be explained by Atkinson’s “huge workload”, which has seen him referee on every weekend of the Premier League season so far.
“Martin’s errors came as no surprise to me,” Hackett wrote in The Telegraph. “Not because he is a poor referee – far from it – but because he has had a huge workload this season and made a dreadful error in his previous match when he sent off West Ham defender Aaron Cresswell.
“Martin has refereed a Premier League match every weekend this season, as well as a Champions League game and a World Cup qualifier abroad. Throw in his fourth official duties on top of that, and it’s not difficult to see why he lacked a bit of sharpness at Stamford Bridge.”
Atkinson's performances in games between Chelsea and Manchester United have provoked controversy in the past.
Sir Alex Ferguson claimed to have "feared the worst" after Atkinson was appointed for a 2-1 defeat at Stamford Bridge in March 2011, yet only made his comments on the official after the match.
United lost to a contentious 80th-minute penalty, scored by Frank Lampard, after Yuri Zhirkov was brought down by Chris Smalling in the penalty box.
Ferguson also criticised Atkinson for failing to send off Luiz for a second bookable offence that day, after the defender tripped Wayne Rooney.
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