The Ligue 1 outfit succumbed to stunning goals from Antoine Griezmann and Haris Seferovic in Tuesday's play-off first-leg encounter, with Milan Bisevac's red card adding to their woes.
Garde conceded that his charges are now up against it for next Wednesday's return fixture, but believes that the Ligue 1 table-toppers can still make it through.
"Real Sociedad's victory is well deserved tonight," he said after Tuesday's match. "They played a very good game. On the other hand, we have not played our best.
"We were always second best in the first half and just couldn't compete.
"My players have given their all but it was not the game that we expected. Not a good result as we are at the beginning of the season. But Real Sociedad are the best team that we have met until now.
"Now there are 90 minutes left. Obviously the mission is not impossible but very difficult.
"We have to try and reverse the scoreline - why not? We will go there with that attitude. Meanwhile, we have a league game coming up so we have to recover."