"I thought the players showed loads of heart," Coleman told Sky Sports News. "They showed loads of commitment and gave everything.
"We knew it was going to be a tough game, even at full strength, then we go down to 10 men too, but the players were absolutely magnificent.
"They dug deep, showed a lot of passion and good organisation, which we had to because they move the ball very well."
Coleman further said that he was "proud" of his players.
"It was disappointing to concede just before half-time from a set play because we've done well from set plays recently," he added.
"But we were in the game at 1-0 and our guys gave everything. You could see they had no more to give at the end, and I'm proud of them."
Wales are back in action on Tuesday when they take on Serbia away from home in their second Group A fixture.