The Liga side were outplayed at times during their last 16 first leg clash with Milan, but an 83rd-minute Diego Costa goal gave them victory at San Siro on Wednesday.
Simeone admitted his side were far from their best and believes they will need to perform to a higher level in the second leg if they want to make the last eight of the competition.
"We started well, then started losing the ball too often and suffered down the right flank," he told Sky Sport Italia.
"We weren't fast enough and struggled to come out, so that helped Milan.
"We changed after the break, Mario (Suarez) got well between the central midfielders and we slowly started to gain more possession, to move up the field and play the game we wanted.
"Everyone knows when you reach the knockouts any mistake can get you eliminated.
"(Thibaut) Courtois performed a great save on (Andrea) Poli, but in the second half we played intelligently in tactical terms and slowly gained our chance to win the game.
"It is a good step but there is much work to do in the Vicente Calderon."
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