Les Gones were beaten 2-0 by the La Liga outfit at the Anoeta on Wednesday, resulting in their elimination from the competition's qualifiers after a 4-0 aggregate loss.
Despite coming out on the losing side of the tie, Garde was full of praise for his side's conquerors.
"During the first 30 minutes we believed we could do something," Garde told reporters.
"We started well and created some chances, I'm thinking particularly about Alex Lacazette's header. At that point we were hoping to get through. After that, during the second half it was more difficult.
"After Real Sociedad scored, everything was more complicated. I think their team was well organised, like they were in the first leg, and they were powerful for 90 minutes. They were a great team - I don't think we faced the weakest team in the tournament tonight."
Lyon have now been without Champions League football for three straight seasons.