However, Kevin De Bruyne equalised for the Premier League leaders on 55 minutes before Sergio Aguero broke Robins hearts with an injury-time winner to put Pep Guardiola's side in pole position to reach the final.
"Very proud of my team," Johnson told Sky Sports News. "Disappointed with their goal late on but the boys were magnificent. We came here and tried to play our game and caused a few problems. You concede possession now and again because of the quality of the opposition. It is only half time and we are well in this tie.
"I said to them 'you've been fantastic. We rode our luck but we broke and got men in the box. The pressing was amazing for the first goal. They can't be disappointed as we are still in the tie. They have shown the world we are good footballers."
"They showed confidence and weren't frightened to be on the ball. Pep Guardiola said to me that we played better than most of the Premier League teams that come to Man City. We will take an awful lot from it and learn a lot.
"It is not over. It will be an interesting game at Ashton Gate. The away goal was very important. We tried to score and certainly didn't park the bus. The lads have to go home and think we can kick on form this performance."
Bristol City return to Championship action at home to Norwich City on Saturday and will host the Citizens at Ashton Gate for the EFL Cup semi-final return leg on January 23.