A challenge from Grant Hanley on Gareth Bale saw the Tottenham star fail to return for the second half while Robert Snodgrass was dismissed for picking up a second yellow card following a lunging challenge on Welsh defender Chris Gunter.
Coleman said: "We knew it was going to be a tough game, it was quite physical, there were one or two brutal challenges but within the rules. I think they were clever, nothing nasty, they weren't trying to break anybody's legs but (it was) get the ball and get the man, in the laws of the game. There is nothing wrong with that, Scotland are entitled to do that."
He added: "I like that, football is a contact sport, I don't want to see non-contact but there were one or two heavy challenges and we guessed there would be but we didn't want to get sucked into that because that is not our game.
"If we had tried to fight Scotland I would have been sitting there with a frown because we would have lost, we had to try and play our game which we did."
Hanley gave the hosts the lead the against the run of play with a header from a Charlie Mulgrew corner in first-half stoppage time but Wales fought back and in the 70th minute Aaron Ramsey levelled from the spot after Snodgrass' dismissal.
Hal Robson-Kanu headed in the winner just over a minute later, with Ramsey ending the game on a sour note when he was shown a straight red card for denying James McArthur a goalscoring opportunity.
Coleman claimed it was a deserved win for his side who now have taken six points from five games with Scotland still sitting bottom of Group A with two.
The Wales boss said: "I thought we dominated the game for 30 minutes and almost became too comfortable, we started having too many touches and invited Scotland back in and they scored just before half-time. I didn't think that was a true reflection of the first half.
"They hit the post in the second half so we rode our luck a bit there but after that it was all us, we dominated possession and created chances and I think we thoroughly deserved to win the game."
- Sports & Recreation
- Robert Snodgrass