Chris Coleman accused Scotland of making some "brutal" challenges on his players after Wales came from behind to win 2-1 in their 2014 World Cup qualifier at a blizzard-bound Hampden Park.
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Defender Grant 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 an earlier challenge from the Blackburn defender on Gareth Bale saw the Tottenham star fail to return for the second half.
Wales fought back and in the 70th minute Aaron Ramsey levelled from the spot after Scotland forward Robert Snodgrass was dismissed for picking up a second yellow card following a lunging challenge on Welsh defender Chris Gunter.
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, who will miss Ramsey and Joe Allen for Tuesday's visit of Croatia with Bale's participation in doubt, 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.
"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."
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."
Strachan, who was "hugely disappointed" at losing his first competitive game as boss, denied his side were over-physical.
"I don't think I saw a bad tackle the whole game, I really don't think so," he said.
"If I felt it was brutal and people were doing anything untoward I would say but I don't think so."
The Scotland boss, whose plans were disrupted when Steven Fletcher had to be replaced by Kenny Miller after injuring his ankle in the second minute, promised changes for the trip to Serbia in midweek.
He said: "It is not an easy period for us. We need to try to win games.
"We will experiment and find out what is right for us and take it from there. It is an opportunity for other people to stake their claim
"The game changed on the penalty. At 1-0, it flattered us but you have to score the second and we had chances to do that but we never took them.
"Steven Fletcher's injury spooked us a bit.
"The penalty causes us a problem, they score right away after that and it is uphill fight after that."
On Fletcher's ankle injury, Strachan said: "His ankle buckled. Fletcher was a bit shocked but he is more relaxed now. He is getting assessed and he will get assessed by his club."
Bale later took to Twitter to allay fears about his fitness.
The 23-year-old Tottenham man posted: "Just clearing the air... nothing wrong with my ankle. I came off at HT due to the stomach virus I've had all week. Should be ok for Tuesday.
"Great win by the lads tonight, hopefully we can take this on to the next game."