Despite being reduced to 10 men in the first half, the Blues grabbed a 2-2 draw to progress 3-2 over the two legs.
"We all believed - not many people did - but we believed as a team," said left-back Ashley Cole. "Three or four months ago no-one thought we had a chance but we always believed. You can't beat that desire, fight and spirit you saw out there."
"We fought for 90 minutes," added keeper Petr Cech. "What we have done is fantastic and we got our reward because everyone gave 150%. We tried to survive and we survived really well."
He said: "Our spirit was outstanding, unbelievable, but the clock wasn't half slow in the second half. It was only when Fernando Torres went round the keeper that we felt we were through."
The Blues will take on either Bayern Munich or Real Madrid on May 19 at the Allianz Arena in Munich.