Swansea boss Paul Clement claimed United striker Rashford conned referee Neil Swarbrick to win the first-half spot-kick converted by Wayne Rooney.
Gylfi Sigurdsson scored a 79th-minute free-kick to earn Swansea a vital point in their battle for survival, but Clement was left fuming at United’s penalty.
Rashford went down under a challenge from Swansea keeper Lukasz Fabianski, but replays showed the United forward trailed his right leg to win the penalty.
Clement said: “The replays showed the player deceived the referee, there’s no other way to look at it.
“You could say he’s dangled a leg to get the contact, but he’s down before that, he’s down before there’s any kind of contact and the keeper pulled out of it.
“I’m not saying cheat. I’m saying deceived. It’s the word I’ve chosen. I would use cheat another time, on this occasion I’m saying he deceived him
“Lukasz was furious. He said ‘I’ve gone down to get hands on the ball, I can see can’t get it, I’ve come away from it, and he’s gone down before the contact’.”
Clement called for video technology to be introduced to decide such issues and said: “It has to be done.
“For me it’s unbelievable, in this day and age, with the technology available, the only people that don’t get help are the ones who most need it. It’s long overdue.”
United boss Jose Mourinho said: “I didn’t watch it but I have Marcus’s opinion and he said that the goalkeeper touched him.”
The loss of Eric Bailly to injury means Mourinho has no recognised central defenders for Thursday’s Europa League semi-final first-leg away to Celta Vigo.
Bailly, Phil Jones, Chris Smalling and Marcos Rojo are all sidelined, while Luke Shaw suffered a fresh injury setback after just eight minutes.
“At the moment we can’t walk from the bed to the toilet without breaking a leg,” said Mourinho.
“We lost players and we lost points, so today was a bad day. We did not look tired and exhausted, we are tired and exhausted.
“This was our ninth match in April, it’s not human. We have a squad of 22 that’s reduced to 13 or 14.”