Head coach Carlo Ancelotti has been rotating Costa and Ribery on the left side, with the Brazilian starting against Freiburg, only to make way for the Frenchman versus Werder Bremen.
But Ribery now faces a two-week spell on the sidelines after suffering a hamstring injury in training.
“Sometimes he played and on other occasions, I played,” Costa told TZ.
“I will now get the chance to show what I can do for the next few weeks. But do not get me wrong, I would have preferred it had Franck not gotten injured.
“Ribery is hugely important for Bayern, but hopefully we can cope with his absence.
“It is obviously a blow, but he must now take his time to get fit again, so he can help us on the pitch once more.”