Ferreira-Carrasco made up for the miss moments later with an inch-perfect pass to allow Germain to slot the opener past Alphonse Areola.
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Monaco looked bright in the early stages of the second half, but were left frustrated as Geoffrey Kondogbia watched his 25-yard strike bring an impressive save from Areola.
Lacina Traore, who was drafted into the team as a replacement for the injured Dimitar Berbatov, should have capitalised on some hesitant Bastia defending just after the hour mark, but Areola continued his good form by tipping the Ivorian's low effort past the post.
Monaco's superiority was finally rewarded 12 minutes from time when Ferreira-Carrasco's free kick found Kondogbia, who held off pressure in the box to head home.
Ferreira-Carrasco then scored the goal that his influential display deserved as he wrapped up the win with a powerful finish at the end of a fast counter-attack from the visitors.