The Magpies were dominant during the opening 45 minutes of the Premier League encounter at The Hawthorns and were ahead at the break through Yoan Gouffran.
"Newcastle were better and sharper than us in the first half," Clarke told Sky Sports News.
"They looked like a side who wanted to secure their place in the Premier League next season.
"All credit to them at the start of the game. They created a number of chance and we were very lucky to hang in there."
West Brom are back in action next Saturday when they travel to Southampton.