A 2-2 draw at home to Bayer Leverkusen ended Atletico's hopes of making the knockout rounds of the comperition.
The Rojiblancos are third on the standings with five points, with second placed Porto on nine.
Diego Simeone's side will have to battle for the Europa League spot with Leverkusen on the final matchday.
With the game locked at 2-2, Yannick Carrasco spurned a great opportunity to win the game for Atletico but saw a late penalty saved by the Leverkusen goalkeeper.
"[It is] a very cruel way [of being eliminated]. It's football," Oblak told Movistar+.
"We have done everything to win, but the previous games have punished us. We have not had the little bit of luck that is needed.
"We can only thank from the bottom of our hearts the support of the fans. They deserve so much more. The team is very sorry.
"It's the fault of the whole team. And not only this match, but also the previous ones. It's a shame that we can't continue in the Champions League."
Simeone added: "In many of the games, we could have scored some more goals with some forcefulness."
"The final action – with the missed penalty, the shot to the crossbar and the shot against Carrasco – sums it up.
"It is clear that we are not looking for excuses, we failed to do things. It makes you angry not to be able to have the possibility of continuing in Porto.
"It is clear that it is a hard blow, we did not expect it, we did not want it nor was it in our project, but it is. There are two ways to continue; either you side with the victim, or on the side of the strong to keep digging."
