France collapsed after leading Switzerland 3-1 in Bucharest, conceding twice as the Swiss forced extra-time before winning on penalties.
Switzerland scored all five of their spot-kicks before goalkeeper Yann Sommer stopped Mbappe's effort to triumph in the shootout.
The Paris Saint-Germain forward was consoled only by Lucas Digne as he trudged off, but his manager came out in his defence - though admitted the miss had hit the youngster hard.
"Nobody can be annoyed with him," Deschamps told French television station TF1.
"When you take the responsibility, it can happen. He is obviously very affected by it."
Switzerland had never won a penalty shootout at a major tournament before Monday - losing their two previous attempts.
Their hero on the night, Sommer, said: "What a match! What an evening of football. It was our chance to finally go through the round of 16, because we never made it before.
“It’s incredible, we played with heart and with character. It’s amazing."