While the Blues have booked their place in the semi-finals with a 5-4 victory on aggregate, they were beaten 3-2 on the night in Moscow due to a second-half meltdown.
The Blues will now be in the draw tomorrow with a potential clash against Premier League sides Tottenham Hotspur or Newcastle United, who remain in the competition.
Read how the 90 minutes unfolded with our minute-by-minute commentary below.
Rubin XI: Ryzhikov; Kuzmin, Ansaldi, Navas, Marcano; Orbaiz, Kasaev, Eremenko, Karadeniz; Natcho, Rondon
"If we had played in Kazan, we'd have a full stadium with fans to support us and of course we'd have more chance to beat Chelsea," BBC Sport quotes Berdyev as saying.
"We have the chance to fight on Thursday. They won in London because we made two mistakes which cost us two goals."
Mikel told the London Evening Standard this week: "No disrespect to the Europa League but when you saw the game on Thursday, it was not [the same]. You get that buzz when you hear the song of the Champions League, it's different.
"We want to be involved in the Champions League again next season. We've been used to it, those kind of special nights, and we want to get it back."
"It's been frustrating to watch [the Champions League games], while we have to play on Thursday nights. I have been here several years and never played football on Thursday nights. So, hopefully, next season we are not going to be in it."