"It was a gamble, but now it is clear that he wouldn't have enough time (to recover his best form after injury)."
Pua was especially angry about speculation in the Uruguayan media that there were political motives behind his brief recall to the squad.
"Some have talked about corruption, some questioned my character. But I have a wife, kids, a family. How will they feel about that?"
Fonseca and the other three excluded players are part of the group that travelled from Japan to Singapore.
Pua left several players resting in Japan who seem poised to start the match against Denmark on 1 June.
Among those missing this warm-up match are Paolo Montero, Alvaro Recoba, Dario Silva and Sebastian Abreu.