When is a foul a foul?

[braboa]

I hear this stuff in the NBA, but you shouldn't really concern youself with the time on the clock when you call a foul, right? Here's the situation, granted it was in a adult mens league play...I whistled a legit foul with .06 seconds on the clock. It was a one-on-one situation A1 fouls B1 on the arm as he attempted a shot going to the basket. Team A had lead by as many as 20+ points early in second half, but Team B came back to take the lead then was down by one when the foul occurs. B1 makes both freebies and they win by one. Afterwards, a Team A player says I shouldn't have decided the game with the foul. Of course my response is that they didn't do what they needed to do to win. Ill advised 3-pt shots that were falling early, didn't fall late in the game. Plus, Team A got into the penalty early in the second half. If I don't call the foul I'm still deciding the game -just in Team A's favor right?