The Reds powered their way through to the knockout stages with a breathtaking display at Anfield, scoring three times inside the opening 18 minutes and adding four more after the restart.
Philippe Coutinho, wearing the armband as Jordan Henderson watched on from the bench, starred with his first hat-trick for the club, while Sadio Mane notched a brace and Roberto Firmino and Mohamed Salah shared one apiece.
"I don't mind too much who we get. Usually I always get Real Madrid so we will see," Klopp joked to BT Sport.
"We have no preferred opponents. It will be really nice [to be back in the knockout stages] after a long time. I love this kind of news.
"Nobody could imagine that it would go like this tonight. It was an all-or-nothing game for both teams.
"Spartak Moscow is a really good side, I know you won't think so now but they are difficult to play against.
"We opened the game perfectly and after we took the lead we didn't have to defend. It was a nice night at Anfield. I have nothing to moan about tonight, it's all good."
Another memorable European night under the Anfield lights... pic.twitter.com/M55tDJg4ll— Liverpool FC (@LFC) December 6, 2017
Meanwhile, Spartak manager Massimo Carrera admitted his team - who would have finished above Liverpool with a win - was not ready for the challenge of such a big occasion.
"I don't want to say that we should have won but our performance showed we lacked quality. It proves that we are not trained for the Champions League level," he commented.
"It's a hard result to take, I've never had a result like this. We have to treat it as a lesson."