Berahino's 44th-minute strike in the contest at The Hawthorns - his second top-flight goal, following up his winner at Manchester United in September - took his overall tally for the campaign to 10, including four goals for England Under-21s.
Talks between the 20-year-old, who is reported to currently be on B£850 a week, and the Baggies over a new deal are ongoing.
And asked post-match for an update on that situation, Clarke said: "We are in negotiations with Saido's representatives and if I was the club, I would get it done as soon as possible.
"He has had a good season, and long may it continue."
Off the back of Berahino's rapid emergence, there has been talk of him potentially breaking into the full England squad in time for next summer's World Cup.
It is not talk welcomed by Clarke, who has been wary of the weight of expectation being placed upon the Burundi-born player.
"It is hard for me if you (the media) want to write about it," Clarke said.
"All I would say is that he is a young boy that, a few weeks ago, nobody was talking about.
"You have to keep the level of expectation down. In this country we are too quick to push people forward as the next big thing.
"For Saido, the most important thing is that he continues to develop as a player.
"That is what I am trying to do with him here and I think he is happy to work with me along those lines.
"My own personal opinion is that he is not quite ready for full international football.
"It is not for me to tell Roy (Hodgson, the England manager) how to do his job, but that is my personal opinion.
"People are trying to push him too far too quickly. Give the boy time to grow and develop."