Terry was targeted by Manchester City fans during the Community Shield on Sunday and Cech believes that the defender can handle the situation ahead of a new Premier League campaign.
"John's a strong lad - but he knows this will go on and on every time we play away from home," the goalkeeper said. "I don't think he was surprised Sunday and I don't think it will affect him in any way.
"All I need is for him to be JT and to play well. As long as he does that everyone will be happy."
Terry has recently denied an FA charge for using abusive and racist language towards Queens Park Rangers defender Anton Ferdinand last October.