The keeper indicated that the 31-year-old knows he may be given a hard time at away games, but suggested as long as his displays are quality, then the Blues skipper will be happy
The centre-back was last month cleared of a racially aggravated public order offence, relating to an incident where he was accused of using racist language towards QPR defender Anton Ferdinand.
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However, the Blues' man could still face action from the Football Association, who are re-opening the case themselves after postponing their investigation while the police inquiry was ongoing.
Terry was the target of taunts from Manchester City supporters during the Community Shield loss at Villa Park on Sunday, something that Cech revealed the defender is now expecting on all away days, however he remains confident the player will be able to continue to produce top displays.
"He's a strong lad." The Czech Republic international said in the Evening Standard. "He knows that this will go on every time we play away from home.
"I don't think he was surprised [by what happened in the Community Shield] and it won't affect him in any way.
"All I need him to be is JT and to play well. As long as he does that, everyone will be happy."
Roberto Di Matteo's men kick-off their new Premier League season with an away trip to the DW Stadium on Sunday where they face Wigan.