"(Khawaja) is a pretty fair cricketer," Cook, who produced a 100-run partnership with Broad, told the Herald Sun.
"Not that I've played a huge amount against him, but he's pretty confident he took the catch.
"Sometimes with these things, you have to take the player's word for it.
"There's no reason for him to say any other, so we trust (him)."
Cook said if the umpire's initial call had been not out he was not sure how things would have played out.
"I don't think we really need to get drawn into those situations — sometimes you do just have to trust the player on that and he was confident," he said.
At the end of the third day's play, England looked to have control of the match, with Cook's unbeaten 244 leading the side to be 491-9, holding a 164-run lead heading into day four.
Cook, who had struggled severely as Australia eased to an unassailable 3-0 lead in the series, posted the highest test score by a visiting batsman at the MCG and his highest score against Australia.
He is also on the cusp of becoming the first Englishman to carry his bat in a test since Mike Atherton in 1997, while it would be the first time an opener from either nation has achieved the feat in an Ashes Test since 1979.