Bristol City: Win was totally deserved
And Johnson praised the determination of his side for going to the Championship side's imposing new Ricoh Arena and outclassing the home team.
"It's nice to come and win a game away from home when you have deserved it," he said.
"We scored two quality goals and played some terrific football throughout. I think all 11 of my players played well and affected the game. They all had an influence, and I am very proud of them all."
Johnson, whose side will now host Premiership Middlesbrough in the fourth round, hopes that Coventry boss Micky Adams is not sacked after the loss.
"I have had a word with him and I wish him all the best, because I think it's very sad," he said.
"I don't want anyone to get the sack. Football has a short memory, and when he first came here he picked up some good results and some good players.
"I believe that if he was given the time then he could turn it around again. But it's all about winning in this business - and it's tough."