Louis van Gaal had no qualms with Lee Mason for sending Wayne Rooney off, but opposite number Sam Allardyce was seething with the officials following West Ham's 2-1 defeat at Old Trafford.
Van Gaal recorded his second win as Manchester United boss thanks to goals from Rooney and Robin van Persie.
A day before the 10th anniversary of his United debut, Rooney blotted his copy book with a reckless lunge on Stewart Downing deep inside the hosts' half.
Mason issued Rooney with his first red card for United in over five years because of the foul, which saw the England skipper hack his opponent down while he was at full pace.
"(It was) the right card for Wayne," the United manager said.
"I could imagine why he did it.
"But I think you have to do it more friendly and that is the only thing that I can say.
"I call that a professional foul.
"Maybe you don't want to hear it but in professional football you make professional fouls."
Rooney will be absent for United's key fixtures against Everton, West Brom and Chelsea.
Given that the international break begins after next week's visit of his former side, Rooney will not play for United until the first week of November.
"It (will be) a great miss, as he played very well and I was very pleased with him, he scored the goal," said Van Gaal, who stated last week that Rooney was the only player in his XI that is an automatic selection.
West Ham boss Allardyce, however, was nowhere near as calm as Van Gaal in his post-match press conference.
Although he was not pleased with Rooney's conduct - he branded the tackle "cynical" and "very poor" - Allardyce's main gripe lay with the conduct of assistant referee Andrew Garratt, who ruled out a last-minute Kevin Nolan header for offside.
Allardyce believes the assistant referee made the wrong call in disallowing Nolan's effort, which he turned in from a Carl Jenkinson cross.
"Unfortunately the assistant referee has dropped a massive b****** and has cost us a point," Allardyce said.
"We had enough chances to get it to 2-2 and we did equalise with a Kevin Nolan goal, but the 'Superman' linesman's x-ray vision is...
"Somebody was suggesting his head's offside. If he can see that his head's offside there then he is a super-human being for me.
"I thought it was onside, I don't think there's any doubt in my mind."
Rooney and Van Persie both beat Adrian with top-class finishes, but the Hammers also posed a threat to the home defence, which contained debutants Paddy McNair and Luke Shaw.
Diafra Sakho headed in to make it 2-1 following a rare error by David de Gea in the United goal and the visitors had plenty of chances to find the net again.
Sakho and Enner Valencia were both guilty of spurning good opportunities for West Ham.
"Our poor finishing has cost us today as well," Allardyce said.
"There were numerous chances to get it back to 2-2 before Wayne got sent off, but we haven't done it. We had 10 men to play against and we still haven't done it."
A grumpy Allardyce then decided to take aim at his defence for slack marking on Rooney and Van Persie.
"In the first half our defending was silly, stupid," he said.
"If we hadn't gifted them two goals I wouldn't be sat here being as frustrated as I am.
"United have gifted players and if you make silly mistakes like we did they will punish you."
Van Gaal, meanwhile, was happy to put last week's 5-3 defeat to Leicester behind him.
After a week of criticism following the capitulation at the King Power stadium, the Red Devils are now within touching distance of the top four.
"We played a very good first half with attractive and attacking football," Van Gaal said.
"I am very pleased with the attitude of my players as they fought to the end."