City were beaten 1-0 at Wembley on Saturday, with Omar Marmoush having a penalty saved by Palace goalkeeper Dean Henderson.
Bernardo told BBC Sport: "It was a huge disappointment for us. We knew we were going to face a tough team. They defend very deep and are very patient, waiting for the right moment to counterattack.
"We lacked a bit more quality in the final third of the pitch to finish the moves. We had a penalty and three or four chances, but today they deserved it. Congratulations to Crystal Palace."
Missing penalties can happen
On the penalty, the midfielder also said: "I don't know. Normally Erling takes the penalty, but they decided to have Omar take it. I wasn't involved in the decision, so I'm not sure.
"Misses from the spot can happen. That wasn't the main problem, although it was obviously an important moment. We still had other opportunities."
Finally, he had emotional words for Kevin De Bruyne, who played his last major final with City: "It's sad that we couldn't win for him. We wanted to give him this trophy, he deserves it. I can't imagine all this success without him.
"He's a great friend, I'm sorry to see him go. I hoped he'd stay longer, but that's life. I wish him the best."