Fourth-placed Paris Saint-Germain, two points behind Lyon at the start, were left with a Europa League spot and drew 1-1 at Lyon's big local rivals St Etienne.
All the other European and relegation issues had already been decided heading into the season finale, where double winners Lille rounded off their spectacular campaign with a 3-2 win over Europa-League bound Stade Rennes.
"Frankly, it's hard. We had to win today," Monaco midfielder Gregory Lacombe told Canal Plus.
"We have lost this final. It's tough, it's tough."
On the day when Formula One cars raced around the streets of the principality in a collision-hit grand prix, Monaco's football side were also crashing out of the top flight with a drab performance.
Lisandro Lopez sealed Monaco's fate seven minutes from time.
The win against Claude Puel's former side, which gave Lyon a place in the Champions League third qualifying round, may not save the coach's job after an average season with reports saying Auxerre boss Jean Fernandez is being lined up to replace him.
"Now we will all go on holiday and come back refreshed and see what is decided. We would like to carry on with this coaching team," Lyon goalkeeper Hugo Lloris said.
Only three points separated Monaco from 10th-placed Toulouse at kick-off in a remarkably tight table for the final day but all the other results became irrelevant given Monaco's demise.
Second-placed Olympique Marseille, destined for the Champions League group stages like Lille, drew 2-2 at Caen to leave coach Didier Deschamps further pondering his options having hinted he could leave last season's champions.
Loic Remy scored a late brace to salvage OM's point.
