Inter were eliminated in the Champions League round of 16 on penalties after Atletico won the second-leg 2-1 to bring the aggregate score to 2-2.
De Vrij said: "We were not the usual Inter, in the first half we conceded the game a bit. We were still dangerous and took the lead, then we immediately conceded the equaliser. We stayed in the game, we had our chances.
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"That's how it went, we went out on penalties and there is great disappointment with how it ended. There is great spirit in this team, we didn't play very well but the spirit is always there, this team always gives its all.
"Unfortunately tonight went badly but we are having a great season. There is work to finish that we started in July, we have to look ahead."