The Corsican side made the most of playing on the counter-attack as seven-times French champions Lyon struggled to impose themselves and made numerous defensive errors.
Bastia opened the scoring just before the break following a Lyon corner when forward Wahbi Khazri was left free to run 50 metres and set up Florian Thauvin who netted again just past the hour in between goals by Anthony Modeste and Khazri.
"This [first] goal is unacceptable. We were incredibly naive," an angry Garde told a news conference.
"Only under-15s can concede this kind of goal. We were far from the level required either in our attacking, defensive or collective display. It's a wreck."
Second-placed Lyon, widely regarded as PSG's only serious title challengers despite relying on young home grown players, have drawn two and lost one of their last three league games.
They are two points ahead of third-placed Marseille, who hold the final Champions League qualifying spot with 51 points after a 0-0 home draw with Ajaccio on Friday.
"We did not have enough heart," added the usually softly-spoken Garde. "Everybody has praised us but I wonder if we can withstand the pressure. Fortunately, this slap in the face will make us move forward."
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