The Sky Blues were stunned by Lyon at the quarter-finals stage.
They will resume their new campaign against Porto on Wednesday night, and Guardiola remains determined to claim City's first ever Champions League crown.
"It was a tough moment, I felt responsible for this," he said. "How the club and players fought - I was not able to drive them on. I feel responsible watching the game, we were not good enough, we didn't play bad.
"We had really good moments but made mistakes and in this competition you cannot do it.
"The reality is every team and manager has to dream with high expectations but the reality is we have not performed to the level.
"We have to accept it with humility, accept all the bad situations, improve and go through and accept a new challenge, start from zero again and try again knowing we have to improve, knowing the demands are so high.
"I feel so bad for the players but this is a new opportunity and we start again."