The Saints progressed into the last four of the competition after first-half goals from Sekou Mara and Moussa Djenepo.
City failed to have a single shot on target in the entire game in an uncharacteristic display at St Mary’s.
Gundogan said he is already looking for a response in the Manchester Derby this Saturday.
“Very disappointing, the result but also the performance,” our captain said.
“It’s definitely not what we wanted. We had hopes of going through in the Carabao Cup but with that performance there was no chance. It was not enough from us.
“There are a few things, a few things against the ball ,we were not aggressive enough, not winning duels, giving them opportunities to play.
“With the ball we made a lot of mistakes, missed a lot of passes, gave them the ball too easily and that resulted in the two goals.
“Today we were not good enough to create chances, not good enough to score a goal. The mix of the performance from all the team gives this result.
“Especially before the derby it’s not an easy one to take, we need to get back on our route, to be humble and work hard, hopefully we can do it better next game.”
The midfielder also reserved some praise for the hosts, who neutralised our threat on the rainy South Coast.
“I’m not surprised at all [with Southampton],” he added. “We knew from past years that it’s always tough to play with a Southampton side like this.
“We knew they would be aggressive and this is exactly what they did. We didn’t have the solutions unfortunately.”
He also expects the Manchester Derby could be as challenging as ever, but is looking for a response from the team on Saturday.
“It’s never easy for the confidence to lose a game before such a big derby,” he said. “We go to Old Trafford, we know we’ve done well there in recent years.
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“It feels like this United side is probably stronger than ever, or especially in the recent past.
“They are full of confidence, they will play good football and we will need a much better performance than today.”
