Gareth Bale's penalty gave the hosts a 21st-minute lead in the World Cup qualifying Group A clash but the visitors hit back strongly and snatched the three points with late goals from Dejan Lovren and Eduardo.
The defeat leaves Wales 10 points adrift of Belgium and Croatia at the top of the group with only four games remaining.
Coleman said: "We were nearly there and we could have gone in at half-time two or three goals up, we had some real good chances, but we could not get that elusive second goal.
"Nevertheless we were 1-0 up and full of confidence, but we sat back and tried to hang on to it a bit soon maybe and invited them on.
"But they are a great team, a really good team, and you can see why they are in the top 10 in the rankings.
"Boaz Myhill made some great saves and we thought it might be our night, but you don't expect a centre-half to score a goal like that.
"It was soul destroying for us. We looked tired and then they got the winner late on when we had probably earned a draw.
"We needed the three points tonight if we were going to do anything in the group and give us an outside chance really. We are not going to qualify now.
"But we can't ask for any more from our guys, we can't. We gave what we had. The second game in a 10-day block is always a tough one physically because it is an intense group. But I can't ask for more from our lads, they gave it their best."
Croatia boss Igor Stimac said: "We were a bit lucky today. Wales were tough. We did not play well in the first half, my players did not do what I wanted, we were not precise moving the ball and we were lucky not to concede more.
"In the second half we came back well. In the end we had more strong players on the bench than Wales and that made the difference today."