Schurrle and Dortmund were wasteful as the German visitors lost 1-0 to Benfica at the Estadio da Luz on Tuesday.
It was a nightmare outing for Pierre-Emerick Aubameyang, who missed a penalty and spurned two other one-on-one opportunities before being substituted by head coach Thomas Tuchel just after the hour.
Aubameyang's spot-kick was stopped by Benfica goalkeeper Ederson 13 minutes into the second half after Kostas Mitroglou's 48th-minute opener, however Schurrle remains upbeat.
"I think we played better, especially in the first half, we had the better opportunities," Schurrle said, via UEFA.com. "Especially with the penalty, we should have won.
"There is a return leg and we will show that we were clearly better then and go through.
"We were clear through on goal and things didn't work out. Such days happen."
Dortmund team-mate Julian Weigl added: "We should have and could have taken more from this game. We put in a top performance, we created many chances. We had to win 2-0, 3-1 tonight.
"A 1-0 defeat is not the best position for the return leg, but we play in our stadium and it is still possible. But it hurts.
"I was fully convinced that one of our chances would go in, we absolutely would have deserved it. I don't quite know what to say, it's really annoying."