Costa did well to finally break through the Baggies defence and picked out the top corner with a powerful effort that left a diving Ben Foster with no chance after 76 minutes for his 12th goal of the season.
Man of the match Costa’s words were relayed to BT Sport by Cesc Fabregas, who effectively interviewed his own team-mate.
Fabregas said after his conversation in Spanish with Costa : “He feels he’s in great form but not the best….so I wouldn’t like to see his best to be honest because he’s playing outstanding.
“But he says that the best way to attack is to defend well and at the moment we’re doing it.
“Yes, they had a few chances at the beginning, but he feels the team is very, very compact and very well organised and that makes it easier for the way we attack.”
Blues manager Antonio Conte was delighted his side’s work ethic finally paid off and had one eye on their next fixture as they travel to Sunderland in the Premier League in midweek.
He said: “When you face this type of game, it’s very difficult to break down and I think we tried to play our type of football and it was very difficult to find space because there were a lot of players behind the ball.
“It was very good and I’m very pleased for my players.
“We have to continue to recover as on Wednesday we have another tough game – but I’m pleased.”
The Italian reserved some praise for Spain striker Costa, adding: “It’s fantastic, his commitment, his work rate – with the ball, without the ball.
“He was very good to win the ball and to score the goal. He’s working a lot for the team.”