Clarke described the win as "terrific", and reserved special praise for goalkeeper and man of the match Ben Foster.
"We played well. It's a terrific win for us. Since the turn of the year things haven't gone our way. To come here and play a Liverpool team, probably playing as well as they have all season, I'm absolutely delighted for the players," said Clarke.
"That's why we spent a little bit of money on [Ben Foster] last summer. We don't spend much at the Albion, but when we do we spend it wisely.
"When [the penalty] was given I thought it was really harsh. It spurred us on. It probably gave us a bit of positive momentum."
The win lifted the Baggies above Liverpool into eighth in the league table.