A newspaper report said Brook was struck by a nightclub bouncer after being denied entry to the venue on October 31.
The 26-year-old subsequently apologised for his behaviour which he felt "brought embarrassment" to him and his team.
Talking to reporters on the eve of their one-day series against Sri Lanka, Brook said he did not consider stepping down but the thought of getting sacked "was definitely playing through my mind."
"I left that decision to the hierarchy and look, if they'd have sacked me from being captain, then I'd have been perfectly fine with it as long as I was still playing cricket for England," the batter said.
Asked if he felt lucky to be still leading the side, Brook said: "Probably slightly, yeah.
"But like I say, even if I had been sacked, I'd have held my hands up and said, 'Look, I've made the mistake' and I'd have been perfectly fine with getting sacked from the job as captain, as long as I was still playing cricket."
Brook said he apologised to his teammates after landing in Sri Lanka.
"I think I've got a little bit of work to do to try and regain the trust of the players," he said.
"I felt like I needed to say sorry for my actions. It's not acceptable as a player, but as a captain it's really not acceptable to do what I did in New Zealand. I'll be the first person to say that. I hold my hands up."
England play three ODIs and three Twenty20 matches in Sri Lanka as part of their buildup for next month's T20 World Cup co-hosted by India and Sri Lanka.
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