Louis van Gaal angrily branded Chris Smalling "stupid" after his dismissal helped City beat United in the Manchester derby.

United were holding their own against their local rivals, but they eventually went down 1-0 thanks to a second-half strike from Sergio Agüero.

City’s task was made much easier by Smalling, who received two yellow cards in eight minutes just before half-time.

Referee Michael Oliver showed Smalling a yellow card for a cynical block on Joe Hart as he attempted to kick the ball down field from his hands.

And the England defender slid in on James Milner soon after, leaving Oliver with no option but to issue him with a second yellow.

Last week Van Gaal called Robin van Persie “stupid” for his goal celebration against Chelsea and this week it was Smalling’s turn to feel the wrath of his manager.

The United manager, who had warned his players pre-match they must not get sent off, told BBC Sport: “In a derby you have to be careful – the second yellow card is a stupid yellow card. As a player you have to control your aggression.

“I didn’t see the first yellow but with the second, you know you already have a yellow, so have to handle it differently. I said that to the players.

“You have to deal with that. You cannot do what he has done with the second yellow card. That is not very smart.”

When asked whether Smalling had apologised to his team-mates, Van Gaal said: “He said it very humbly. You can only accept it. But nevertheless it was in my opinion not so smart.”

Smalling impressed against on his return from injury against Chelsea last week and he was playing relatively well before his two moments of madness at the Etihad Stadium.

Van Gaal’s anger towards him is likely to have been heightened due to the fact that United are already severely depleted in defence.

Marcos Rojo will join Phil Jones and Jonny Evans in the treatment room this week after he hurt his shoulder sliding in for a tackle in the second half.

"He has dislocated his shoulder," said Van Gaal, who ended the match with Michael Carrick and Paddy McNair at centre back.

“He won’t be available next week. We have lot of injuries in defence.”

City launched wave after wave of attack at the United goal following Smalling’s sending off and the visitors finally crumbled when Agüero turned home Gaël Clichy’s cross in the 63rd minute.

City should have added more to their tally, but they suffered a bout of nerves towards the end of the match, when Marouane Fellaini and Van Persie had good chances to level.

That did not matter much to Manuel Pellegrini, who was happy to see his team end their three-match winless run.

“I am very pleased with the performance. It is always important to win a derby, especially against this Manchester United team which is a great team with great players,” Pellegrini said.

“We played really well all the match except the last 10 minutes with less intensity but I am really happy about the result.”

Pellegrini’s only gripe was with referee Oliver, who waved away several penalty shouts.

The most plausible appeal came in first-half injury time when Rojo kicked Yaya Toure as he was about to shoot from 10 yards following a masterful chip by Agüero.

“It is unbelievable we didn’t get a penalty (for the foul) against Yaya Toure,” Pellegrini added.

“It was not only a penalty but also a sending off because was the last man.

“There were two others against Sergio but we are not talking about that.”

Pellegrini’s men now trail leaders Chelsea by six points. United’s plight is far worse.

United have four points fewer than they did at this stage last season, and Van Gaal has had a far easier run of fixtures than his predecessor David Moyes, who was sacked after 10 months.

Van Gaal remains adamant he is taking United in the right direction though.

“In spite of all the injuries we are very close (to the top teams in the league),” he said.

“We were very close against Chelsea and we were today, but we have to make steps to improve.”

Van Gaal thinks a spell towards the end of the match, when Fellaini spurned two chances and Van Persie drew a good save from Hart, shows his team have a lot of fight in them.

“In the last 20 minutes they showed a will power that was unbelievable,” he said.

“We could have scored. In the first half we gave the ball away too easy.”