While the situation TerFu paints happens too, this was not the case in your game. Your guys had many fouls way before the last minutes of the game, so this was not the cause.
Some of your guys are very foul prone, especially Neset, Cesarczyk and Baamonde. If you look at this or previous seasons, you'll see they average around 1 foul for every 10 minutes they play. This game was no different for those guys, they fouled a lot. This is caused by a hidden trait referred to as "Aggression trait"; it affects how often a player fouls and is fouled by others. For your other guys, it could be they defended a player that have the trait that they draw fouls easily, or it could be just a bit of bad luck too.
You can't do anything about the aggressiveness of your players, what you can do is pay attention to they amount of fouls a player makes when buying a player. You can also try to switch matchups if you see that one of your opponent's players gets to the FT line a lot; then you can put your foul prone player on another player to prevent him from fouling out quickly.