"I don’t want to offend his upbringing or his parents ... but he looks gay," Taylor said of Costello in June.
"There’s nothing wrong with that, it's just a look, as 'sophisticated' is a look, as 'daggy' is a look. You look gay."
The comments prompted 3AW to counsel Taylor, the radio station's general manager Shane Healy told AFL.com.au.
"He was spoken to, yes, by our legal counsel and also by our national news director at the time," Healy said.
3AW relieved Taylor of his radio commentary duties for Sunday's MCG blockbuster as the fallout continued from Saturday night's controversy.
"Because there'd been a previous transgression on AW a few weeks ago, I couldn't have a situation where he wasn't in some way shown to be penalised (for his comments about Harry Taylor)," Healy said.
"I told him I didn't want him calling the game today."
Healy asked Taylor to apologise to the station's listeners on Sunday.
"We said we'd like him to come on air and give clarification on the apology from last night – because that was on Seven," Healy said.
"Because obviously he's a key part of our broadcast team we felt that it was important that he did it to our listeners as well.
"At the same time, because he'd made what I'd say was a serious gaffe a few weeks ago when I was overseas with a comment about Seb Costello.
"Then this one following it up pretty soon after, after being counselled, I felt from the radio station's point of view that we needed to make a stand.
"So we said he wouldn't be calling today."
Taylor said he regretted his "choice of words" in his apology to 3AW listeners.
"I've spoken to (3AW) management and they have chosen to give me the day off to collect my thoughts today, so I'll take the opportunity to have a day off," he said.
"My apology of last night absolutely stands unequivocally.
"I made a blue, I apologised accordingly at the first opportunity to the Seven viewers where I made the blue.
"I regret my choice of words that I used on the night and I will receive some high-level counselling off the people at Seven, which is fantastic.
"And I've also spoken to Harry Taylor today and apologised to him, even though my understanding from that conversation (is) that he was personally not offended by any of the comments.
"So on top of that, 3AW have chosen to give me the day off today to collect my thoughts."
Victorian footballer and anti-homophobia campaigner Jason Ball said Taylor's apology to the Cat player showed a lack of understanding of the broader picture.
BT's apology *to the player* completely misses the point. Shows no understanding of the impact homophobic language has. Education needed.— Jason Ball (@jasonball88) July 12, 2014
Channel Seven said comments such as Taylor's were "unacceptable and should not and will not be tolerated".
"Brian has been censured, and will be supported through counselling and education to ensure this mistake will never happen again," Seven managing director Lewis Martin said in a statement.
The AFL contacted Martin soon after Taylor's comments and expressed the League's view that the comments "were completely inappropriate, needed to be withdrawn and an apology issued".
Martin told the AFL that process was already underway.
League spokesman Patrick Keane said the AFL had no plans to take any further action against Taylor.
3AW's Healy said Taylor would most likely be back on air for the station on Monday.