West Brom, ranked as outsiders at the start of the season, moved into third place in the Premier League - at least until Chelsea met champions Manchester City on Sunday - after winning a fourth successive league match for the first time since 1980.
Clarke told the BBC his side had dominated the game, adding: "I thought we passed the ball brilliantly and managed to pick them off. To score four goals against any team is a great performance.
"The players deserve all the credit, they've worked really hard; people have had to sit up and take notice and the Albion fans can enjoy this spell."
"To talk about European football at this stage would be folly, there are a lot of games to go so we'll keep our feet on the ground," he said.
Honours and European places may still be some way off but West Brom's form this season has been excellent, with Clarke building on the foundations put in place last season by Roy Hodgson, who left the club to manage England.
Sunderland's goals came from Craig Gardner and Stephane Sessegnon. While West Brom climbed to third, Sunderland stayed close to the relegation zone, with 12 points from 12 matches.
