Clarke was part of Dalglish's backroom staff at Liverpool, but when the Reds parted ways with the Scot, the former-Swansea boss Brendan Rodgers was hired by the Anfield hierarchy.
But Cech reckons Liverpool missed out by overlooking Clarke, who spent more than 10 years at Stamford Bridge as a coach.
"I was surprised that it took people so long before he actually got the job because I would have thought that he might have got his chance already when he was at Liverpool," said the Chelsea keeper in the Fulham Chronicle.
Liverpool instead turned to Rodgers, although Wigan boss Roberto Martinez was also reportedly considered.
West Brom hired Clarke this summer, and Chelsea travel to the Midlands this weekend to face their former-coach.
Clarke's West Brom have been superb at home, winning five from six matches. The Baggies dispatched Liverpool 3-0 on the opening day of the season and Chelsea are likely to be in for a tough afternoon, although West Brom will be without on-loan Blues striker Romelu Lukaku.
Liverpool face Wigan this weekend, and Brendan Rodgers' side will be looking to avenge last season's 1-0 home defeat to the Lactics.