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 semi-finals are Bayern Munich, Real Madrid or Atletico Madrid as Chelsea chase their second Champions League title.
Schurrle, 23, is unfazed about who Chelsea draw on Friday for their semi-final tie.
"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 said.
"Every team in the semi-finals 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."
Having Mourinho in charge shapes as a huge advantage for Chelsea, with the Portuguese tactician previously guiding Porto and Inter to Champions League crowns.
Mourinho has still never lost a Champions League quarter-final tie, and Schurrle hailed his influence in their 2-0 second-leg win over PSG.
"It is unbelievable. 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," Schurrle said.
"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 utilised 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."
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