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.
|11/2||Chelsea are 11/2 with Bet365 to win the Champions League|
And 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 told reporters.
"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."
Mourinho boasts a stellar record in the Champions League, having made the semi-finals in eight of his 10 full campaigns and triumphed with Porto and Inter.
The Portuguese 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," 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," 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."