Morgan Amalfitano gave the Baggies a 54th-minute lead, but Wayne Rooney equalised just three minutes later. However, the England Under-21 forward Saido Berahino scored a famous winner for his side with little more than 20 minutes remaining.
West Brom held on to secure victory and Clarke said after the game that the attention should be on the performance of his side.
"It is great and fantastic for the players," the West Brom boss told Match of the Day.
"Today my one wish is the players are getting the credit and we are talking about how good we were and not how poor Manchester United were.
"We came here not to sit and defend but to come out and go for it. We made some late additions in the transfer window and now hopefully are fans can see we can have another good season."
The result was West Brom's second successive league victory and has seen them climb to 10th place in the Premier League table.