The striker, who scored in the second half of his side's 3-2 defeat, says the captain's sending off was both incorrect and costly in their exit from the competition
The Argentine forward, who scored in the second half, said he was not in the habit of criticising match officials, but felt referee Chris Foy had made a mistake in sending off his team-mate early on in his side’s dramatic 3-2 loss.
Aguero wrote: “I seldom try to find excuses or comment on the referees but the unfair expulsion of Vincent Kompany conditioned the whole game today.
“I want to thank the fans of Manchester City, who inspired us. If we stand together, both fans and players, we can achieve important feats.
“Despite losing, I believe we leave the field strengthened. We almost equalised against all the odds. With this attitude, anything is possible.”
Kompany himself posted on the social networking site and although he didn’t comment directly on the decision he said he felt City were the moral winners of the clash after a stirring comeback with 10 men.
He said: “Thanks for the support I'm getting from everyone. I’m surprised at Sir Alex Ferguson's post match comments. Maybe that is a sign...
“The fans, the players and every single person involved with Man City FC were incredible today. [We were] definitely the moral winners of this game.”
Defender Micah Richards added: “We lost today but in our heads we won! Our team spirit is inspirational! The fans kept us going for 90 minutes! Thank you.”
Winger Adam Johnson also felt the hosts had been unlucky not to progress in the competition after an enthralling contest.
The England man said: “Great effort today!! [We were] so unlucky... fans and everyone involved were excellent!”
"We might have lost the game, but we won more respect among each other, for working that extra yard. Thanks to our fans for their support," wrote midfielder Nigel de Jong.
As a result of their victory at the Etihad Stadium, United’s reward is a tough test to Anfield where they will play their other fierce rivals, Liverpool, at Anfield.