Gomez is sidelined with an injury suffered in pre-season and will miss the start of the Bundesliga this weekend.
He told TZ: "Bayern is not a kindergarten, where everyone is just pampered.
"Everyone wants to be cherished, but first you have to prove yourself and then keep on doing so. If you do produce the goods, you will be rewarded.
"Gomez, like everyone, will have to deal with the fact that there is competition at the club."
Bayern begin their league campaign away to newly-promoted Greuther Furth on Saturday, August 25.