The Blues will face Bayern Munich, Real Madrid or Atletico Madrid in the semifinals but the Germany international believes they can beat any team left in the competition.
Jose Mourinho's men overturned a two-goal deficit to edge past Paris Saint-Germain in their last-eight tie on Tuesday.
Awaiting in the semifinals are Bayern Munich, Real Madrid or Atletico Madrid as Chelsea chases its second Champions League title.
"I don't think we're underdogs. We can win against every team. That's how we will manage, no matter who we get," the German told reporters.
"Every team in the semifinals can win this. It's one step to go to the final. We'll see who we get and we'll see if we can go through."
Mourinho boasts a stellar record in the Champions League, having made the semifinals in eight of his 10 full campaigns and triumphed with Porto and Inter.
The Portuguese has still never lost a Champions League quarterfinal tie, and Schurrle hailed his influence in a 2-0 second-leg win over PSG.
"It is unbelievable," he added. "This statistic tells you that he knows what to do. He plays a big role. We had many meetings. He knew the situation. He gave us advice.
"Almost every time we've played at Stamford Bridge, we've scored two goals. We only needed two goals [against PSG]. That’s what we did. We utilized the plan. He told us to be patient - we needed patience because everybody wanted to go, go, go, go. Afterwards, in the dressing room there was so much emotion. Everyone was dancing, screaming."