Roma pipped Antonio Conte's men to top spot in Group C by beating Qarabag 1-0, while the Premier League champions only salvaged a point through Stefan Savic's own goal after Saul Niguez had put Atletico on course for the win they needed to stand any hope of staying in the competition.
With English teams leading four of the other seven groups, Chelsea's only possible last-16 opponents as it stands are PSG, Barca and Besiktas.
Hazard overcame early rough treatment to work at the heart of Chelsea's attacking threat, but Jan Oblak delivered a fine display in goal, and the Belgian is sure they can do better, no matter what calibre opposition they face in the next round.
He told BT Sport: "It's not a problem, we are Chelsea!
"We are a top team, so we can face any team. We know PSG and Barcelona are very good but we are Chelsea so we have to be ready for everything.
"We can do everything!"
Hazard was satisfied that Chelsea had done more than enough to win after taking 17 shots on goal, but highlighted their main obstacle: "The only problem, the goalkeeper was on fire.
"We should have scored more goals, won the game and finished first in the group, but we draw.
"But it's a good draw because Atletico played well they are very strong so we are happy today."
Blues captain Gary Cahill was also quick to hail Oblak, reserving particular praise for a desperate intervention between him and Jose Gimenez to deny Alvaro Morata.
"Their keeper was fantastic today, especially the one where he's took one in the face, I'm not sure how he's kept that out," the England man added.
"He's had an amazing game, which has got them a point."