Wales had 57% of possession in Bucharest and managed nine shots on target.
But the likes of Ethan Ampadu, Brennan Johnson and substitute Lewis Koumas were guilty of spurning chances.
Defeat means Wales are without a win in four matches in 2026, with their stunning 7-1 triumph over North Macedonia in November the last time Bellamy’s men tasted success.
His side return to action in Nations League A – where they face Portugal, Denmark and Norway – later this year.
Wales goalscorer Brooks says the team need to be “miles better” in that campaign.
“We were not good enough, not at all,” Brooks told BBC Match of the Day Wales.
“We need to watch it back and try and take some positives out of it.
“We kept the ball quite nicely, but we lacked penetrating passes.
“We played in the wrong areas. We need to be miles better in the Nations League and in the next camp.”