The La Liga giants have managed just two points from their opening two Group C encounters, leaving them three points adrift of second-placed Roma, who are in action against leaders Chelsea.
That means anything less than victory at home against Qarabag this evening could spell disaster, and Simeone is hoping to avoid that possibility at all costs.
He said: “Our success in the last few years in all competitions means that if we don't get an excellent result there's criticism, but we need to live with that if we want to achieve excellence.
“We have a responsibility tomorrow. It's an important match for the club, the fans, the players, me.
“We'll play it knowing this. We want to do well and carry on growing and will go into it like that.”
Simeone added: “The boss is always responsible for what happens on the pitch. I'm not shirking any of that.
“We haven't started that well in the Champions League. We deserved to win in Rome and Chelsea were very good here.
“We've done better in the first meeting between these two sides [which ended 0-0]. We've got a marvellous opportunity in front of us and we're ready for it.
“You always fret over results. Any coach will tell you that. You always want to improve, to win, to reach the club's objectives.
“We want Atletico to be amongst the best sides in the world. It'd be bad if I wasn't worried - if I were relaxed then that would be bad.”