Despite victory over Botafogo on Monday, Atletico failed to qualify from their group.
Afterwards, Simeone said: "We were in a very good group with the Libertadores and Champions League winners. We scored the same number of points. I think today was the most complete match.
"We played in the opponent's half for a long time with plenty of space to defend, and we couldn't convert the chances we had to stay in the group. The PSG match, from 2-0 to 4-0, with the goal that was disallowed and the penalty that wasn't awarded today due to an action for unknown reasons, clearly meant that the situations didn't favor us.
"It's part of football. Sometimes they favor you, and other times, no referee decision."
Season caught up on us
Reflecting on the group campaign, the Argentine continued: "We knew beforehand that it was a very beautiful and exciting tournament, but for the Europeans it catches up with us at the end of the season and for the South Americans at the very end. I didn't like the first game beyond the result because we weren't compact.
"In Seattle we showed a better face in the first half and today we played like we usually do, intense, looking for goal-scoring chances, situations that didn't go our way and we didn't have the goddess fortune to score a goal. We're not in the zone where PGS and Botafogo are, but we got the same points as the Libertadores and Champions League champions and we were eliminated.
"That's the beautiful part of football, it tells you that we're close, but we're always missing a little more."
Saddened to be out
Simeone added: "I'm saddened to have been eliminated. The objective was to continue and we couldn't achieve that.
"We got six points, won two out of three games, competed from less to more and this time we had to be eliminated due to goal difference in a difficult group. Nobody cares about all the talk.
"Tomorrow you'll be out of this tournament and it hurts because we made a lot of effort to be able to reach a La Liga with Barcelona and Real Madrid and to spend four years in the Champions League with better numbers than one of them. We were more excited than we actually did."