A header by midfielder Youssef El-Arabi five minutes from time silenced the Velodrome stadium and gave the visitors from Normandy a stunning victory.
Marseille, who secured their first league crown since 1992 last May, looked nervous throughout the match but seemed to have escaped with a draw after a late equaliser from substitute forward Mamadou Samassa until El-Arabi struck.
"Caen were very determined and deserved to win but we showed many weaknesses," Deschamps told reporters.
"We made errors and lacked determination," he added. "We were the favourites and should have won that match. Now we know we need reinforcements if we want to be competitive."
Last season's runners-up Olympique Lyon also struggled, managing only a 0-0 home draw with Monaco, although they did step up a gear after the break and created several chances.
Superb volleys from Paris Saint-Germain's Benin midfielder Stephane Sessegnon and newcomer Nene helped secure a 3-1 home win over St Etienne that made the Parisians early leaders.
"We need to do more than that in the future and we had a few problems at the back but it's encouraging," said PSG coach Antoine Kombouare, who struggled last season with frustrating results against a backdrop of violence from their unruly fans.
