Charlton ended a three-game losing streak with victory against the league-leading Blues on Saturday.
Jones took charge of the club in February and steered them to a 16th-place finish.
He told fans to trust him to run the club and pick the team, and suggested he would leave if this did not happen.
“People don’t know what happens through the week, people say ‘he should be playing’,” he said.
“He might be carrying an injury, something might have happened in training.
“If people want to trust us and trust me to manage the football club then fine, if they [the fans] want to pick teams themselves, then come in, I’ll have my money and I’ll move somewhere else if that’s what needs to be done.
“I see them [the players] every single day and we pick a side we believe can win the game.
“Sometimes players let us down and players let us down [on] Tuesday, absolutely let us down.
“I took responsibility for that but we bounced back today with a wonderful performance and I’m really proud of the football club.”