The second-tier outfit progressed through to the quarter-final stage of the competition for the first time since 1989 with a convincing comeback victory at Ashton Gate on Tuesday.
Johnson believes that the introduction of Milan Djuric on the half-hour mark acted as the turning point in the match, with his side recovering from behind by netting a couple of goals in either half to keep their Wembley dream alive.
"I thought it was an outstanding game of football," the club's official website quotes him as saying. "I thought Crystal Palace showed their Premier League class in the first 15 to 20 minutes. I didn't think we started well though, we didn't hold the ball well up front or get our game going at all.
"After that, basically when Milan Djuric came on and for the first part of the second half, I thought the boys were outstanding. There was quality, energy, good football and two outstanding finishes. It was amazing.
"Did it flatter us, probably a little bit but we saw at the end we were keeping the ball, stringing 20-30 passes together and it just goes to show that when we are at it, we can compete with the best.
"Milan started getting hold of the ball, allowing the midfield to join the play and I thought Josh Brownhill was absolutely fantastic today. He looks like an unbelievable signing. He was running rings around Premier League players so I'm delighted for him but to a man, everybody played well."
City have now knocked three Premier League sides out of the competition, having also overcome Watford and Stoke City in rounds two and three respectively.