Coleman did not condone Neil Taylor's red card tackle which broke Seamus Coleman's leg but objected to the suggestion Bale could also have been sent off for a tackle on John O'Shea.
Bale was booked and is now suspended for Wales' trip to Serbia in June.
"The ball is there to be won, he's got to go for it," Coleman said.
He continued: "But come on, were all the bad challenges on that pitch ours? Is Gareth [getting criticised] because it's Gareth Bale? Or was it genuinely bad?
"If I see it again and I see it differently I'll apologise for getting it wrong, but there wasn't a hint of it in the dressing room of getting one wrong. He actually wanted to appeal the yellow card.
"If it is a bad one from Neil, it's a surprise because he's not that type of boy, he's been there before with a bad injury. I just hope Seamus is going to be back sooner than later.
"Neil went [to apologise to Coleman] at the end of the game, across to where the Republic's home changing room is. I'm not sure he got hold of him but he went over there."
The draw in Dublin was damaging to Welsh hopes of qualifying for the 2018 World Cup, leaving them third in Group D and four points behind joint-leaders Serbia and the Republic of Ireland.
In a fractious post-match media conference, Coleman was asked by Irish journalists if Bale should have been shown a red card for the foul.
"In your view do you think one or two of yours [Irish] were lucky to stay on the pitch? Because there was a little bit of both," he said.
"Your boys weren't coming off with halos on their heads. It was going on all through the game. I'm not complaining - it was a typical British game of football.
"You don't want to see anyone getting sent off. There were one or two complaints from our boys - your boys were a little bit late here and there, and so were our boys, so I'm not complaining. That's football."
Wales boss Chris Coleman has defended Gareth Bale and his team-mates after their ill-tempered goalless draw with the Republic of Ireland.