Is the exchange of a rook for two minor pieces really worth it? I recently played a game with my friend I wish I had memorized the entire game, but, unfortunately, my memory isn’t too good.

In summary, I was in a really tight position, and playing as black. I had a very active rook on the open f-file However my opponent was attacking my king. and it looked really bad. As a result, I sacrificed my very active rook for a bishop and a knight. I still lost the game, however.

Is that kind of exchange worth it? Once I lost my rook, my opponent was able to monopolize on the f-file by making a triple battery, and consequently I lost.

Also, when is it a good idea to make sacrifices concerning Rooks and minor pieces?
You say your opponent had a strong attack against your king and you had to "sacrifice" your rook for two minor pieces and went on to lose. I think you have it the wrong way round. It sounds like your opponent had a strong attack against your king and sacrificed two minor pieces for your rook, your one active piece by the sound of it. 

In general a rook and a pawn are roughly equivalent to two minor pieces. However in the middlegame this is usually not a good trade for the player losing the two minor pieces because two minor pieces are two pieces which can attack/defend whereas one rook is only one piece which can attack/defend and the number of pieces participating in the attack or defence is generally more significant than their precise power.