Gunn, who was appointed manager in January until the end of the season, saw his side lose 4-2 at already relegation Charlton Athletic on Sunday and slip into the third tier of English football for the first time since 1960.
"I want to be involved next season and I will be speaking to the owners and directors over the course of the next few days," he said.
"It's devastating, but we have to fight back and we'll start to fight back tomorrow.
"I need to find out which players want to represent Norwich City in League One next season.
"The club and the supporters have been let down. To go out on a pitch and capitulate like that is not good enough."