The head coach failed to deliver a play-off final against Italy next week after suggesting his team had made an error in trying to protect a 1-0 lead instead of adding to it.
Wales had led 1-0 from the 51st minute until the 86th minute when Edin Dzeko equalised, before a goalless extra time led to a 4-2 defeat on penalties.
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“For the last 20-odd minutes of the second-half, we started protecting, and we can't protect,” said Bellamy.
“It's not what we do. We have to play with the ball, we have to keep the ball, and then we'll gain more chances.
“We just had that little spell where we tried to see it out and it allowed them to get more plays into our box, hit bigger diagonals, and then they score from a set play.
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“We weren't really able to press during that time, which allowed more longer balls to come in because we weren't keeping it. It got chaotic, and that was the bit we don't want with this team (Bosnia).
“They're drilled for chaos. And we allowed chaos to creep in for 20 minutes. We've tried to see it out but we're not built that way. We don't play that way.”
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In the short-term there will be financial implications for Wales and the FAW from not making it to the USA, Canada and Mexico this summer.
It will mean a £10m windfall won’t be landing in the coffers and that will have an impact on the development of young talent.
There will also be plenty of speculation over Bellamy’s own future, with less than two years now remaining on his contract and having been linked with a number of clubs.
In the short-term, Bellamy will have to lift his players for the worst consolation prize imaginable - a game against an equally deflated Northern Ireland team at the Cardiff City Stadium on Tuesday, which is now a meaningless friendly rather than a shoot-out for a place at the World Cup.
Bellamy admitted it will be difficult for his players to recover quickly from their disappointment and added: “it really hurts for them because to get to back-to-back World Cups was really our target.
“And to know you've not got there, and when you see players really disappointed, yeah, it hurts you more.
“But I said to them in a huddle, this is going to keep getting better. This is going to keep improving.
“As a team, I believe this team will keep improving. And I believe players coming into it are going to enhance the Welsh team as well.
“It will be difficult to sleep off the back of this one.
“But it makes me even more determined. Tomorrow, the sun will rise.
“And I'm going to watch that sunrise tomorrow. And then straight away, how do I go again? How do I improve? How does the team improve? How do we get better?”
