Dragovic believes his side can make it an English hat-trick by beating Chelsea to claim a place in the final.
The club knocked Manchester United out of the Champions League last season and beat Tottenham in the last eight of the Europa League earlier this month.
Dragovic said: "With a bit of luck in the game we can compete against any team. Of course last year it was Manchester United and then it was Tottenham this time.
"This [playing Chelsea] is for the whole team an indescribable thing. We have worked hard for it. For each individual there is a huge feeling, we are extremely pleased at this game.
"You get it already with how the whole town is talking about the game. You can feel that the whole region of Basle, and even the whole of Switzerland, is behind us. We will, of course, try to represent FC Basle as well as possible.
"I could list more players, we look at everything, but we want to be able to enjoy the two games against them."