The visitors defended resolutely, helped by a stunning show from goalkeeper Ben Foster who saved Steven Gerrard's penalty, before stunning the Reds with Gareth McAuley and Romelu Lukaku scoring in the final nine minutes.
It was a first league win in seven to lift them above Monday night's opponents into eighth spot and Clarke told Sky Sports: "It's not been the best start to the year so it was good to come here and play well. It was a terrific win.
"Things haven't gone our way this year. We've been producing perfectly decent performances but we've not been getting the results. But to come to Anfield and beat a Liverpool team who are probably playing as well as they have all season is great.
"To get that kind of result and level of performance from the players...well, I'm absolutely delighted. They have put in so much effort to get that reward."
On the penalty kick awarded for a clash between Jonas Olsson and Luis Suarez, Clarke said: "When it was given, I thought it was really harsh. I've since spoken to people about it and they say it's worse than harsh!
"When Ben saved that penalty, it gave us a positive momentum and I think we started thinking we could win the game. But we've always been one result from kick-starting the season again.
"Hopefully that result came tonight and we can kick on from here and start chasing the teams above us."