"Diego Costa gets in your face, he wants to bully you so you have to stand up to him," Shawcross told the BBC.
"He is a fantastic player who plays close to the line, so to keep him quiet is fantastic.
"We have a fantastic spirit and a good team now.
"Look how many Champions League winners' medals we've got in the squad now."
Mourinho 'gives up' on stadium ban appeal
The defeat piles more pressure on Blues manager Jose Mourinho - who was banned from the stadium for today's game.
Chelsea slip to 16th in the Premier League after enduring their seventh loss of the campaign.
Invalid email
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy