The non-league side defeated Premier League outfit Norwich City 1-0 at Carrow Road in the fourth round of the competition on Saturday.
"I would like to think the next round will be on TV," the Daily Mail quotes him as saying.
"It's only right. We're the only non-league team left in the competition. Any draw is a big draw for us. If the TV cameras had come on Saturday, they would've got great TV.
"They probably didn't think we could do it. I'm sure we'll get it in the next round. It'll give us great coverage and put smiles back on the fans' faces after some terrible years."
Luton are currently sixth in the Conference Premier table.