Former Watford chief Adrian Boothroyd took over the reins on Wednesday, having been spotted in the stands at the Priestfield Stadium on Tuesday as Gillingham won on penalties following a 1-1 draw in the Johnstone's Paint Trophy.
"I have massively enjoyed my time here and it's given me the opportunity to realise my ambition, if only for a short time," said Dunne after the match.
"I've got a fair idea of who the manager is and I am sure some other people do with all the rumours flying around but it's not for me to announce it.
"I can promise you I'll be here doing whatever the new manager wants me to, I am 100% committed to this club."
On the game, he added: "We had some really good passing and some brilliant approach play, we just need to be more decisive in the last 20 yards and we'll score a lot of goals this season."