Atletico reached the quarterfinals after a penalty shootout.
Saul came on in extra-time and saw his penalty saved by Inter goalkeeper Yann Sommer.
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He later posted to social media: "Honestly, it is difficult for me to write right now, but just as I write in the good times, I have to do it in the bad times. It is a s****y moment for me on a sporting level, and I am aware... I accept all the criticism and not only because of today's penalty but because of how I am at the moment.
"I don't know exactly what it is, but the only thing they have taught me is to continue working through the good times and the bad until we manage to change the situation. Thank you for being there in the good times and the bad.
"Apa Atleti!"