The reigning Premier League champions, who have won six EFL Cup titles since 2014, suffered a 2-0 loss at St Mary’s.
Man City are currently 18 places above bottom-placed Southampton in the Premier League but were knocked out by Nathan Jones’ side, who progressed thanks to first-half goals from Sekou Mara and Moussa Djenepo.
While Manchester City boasted more than 70% possession, they failed to have a single shot on target.
Guardiola said: ‘The better team won. We didn’t play good, we didn’t play well in the beginning. There are many games you can start not good and overcome and we didn’t do it.
‘When you are not prepared to play this game you arrive one inch late and don’t score a goal. When you are prepared you score the goal.
‘Today was a bad night, the opponent was better so we have to congratulate them. To win games you have to deserve it and tonight we didn’t deserve it.’
Former England striker Chris Sutton, meanwhile, heaped praise on Southampton after they booked their place in the EFL Cup semi-finals.
He told BBC Radio 5 Live: ‘Southampton absolutely brilliant this evening! Nathan Jones needed a performance like this, especially against the big boys.
‘Southampton coped really well after going 2-0 up, Gavin Bazunu barely had to make a save.
‘Nathan Jones needs time, he took over an absolute mess. The negativity really took over after the defeat against Forest when they didn’t have a shot on target.
‘After the win at the weekend [over Crystal Palace in the FA Cup] there was still some scepticism. If they can play like they did today with that intensity then they will stay up and it is a big if. But it is fantastic for Nathan Jones tonight.
‘It wasn’t just that they beat Manchester City it was the manner in which they did it. They were brave, pressed Manchester City high and forced them into errors.
‘They get themselves in front, the performance in the second half after they went to three at the back was fantastic.’
Southampton’s reward for beating Manchester City is a EFL Cup semi-final against Newcastle United. Manchester United face Nottingham Forest in the other fixture.
Saints captain James Ward-Prowse said: ‘A special night. These games are special to play in especially when you’re struggling in the league.
‘We knew this was a distraction from the league and a great showcase. We showed no fear.
‘It’s always tough when you’re in the position we are. The manager has been excellent and has given us fresh ideas and new energy. He wanted us to be bold and aggressive.
‘We have been guilty in the past of having a result at half-time and dropping off. We showed a different part of our game. We thoroughly deserved the win.’
Southampton boss Jones added: ‘Really proud of the football club tonight. Proud of the players and the coaching staff for making strong decisions under pressure.
‘Their manager is the most innovative, he will always have solutions. The changes we made brought energy and we saw out the game. We weren’t hanging on, we were a threat at times so I am really proud of the team.
‘The team hasn’t scored enough goals. We have to be a more potent force. Sekou [Mara] scored his first goal and that is brilliant. We want to be a front-footed side that keeps clean sheets and scores goals.’
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