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According to the stuff.co.nz website, while England were underwhelming in their recent drawn Test series with New Zealand, their woes paled in comparison to those of an Australian side thrashed 4-0 by the same India side Cook's men had beaten 2-1 just three months earlier.
Michael Clarke's team passed 400 just once in eight innings and never got close to dismissing India twice, but Cook expects them to be in far better shape come the first Test at Trent Bridge.
"Everyone would be slightly foolish to think that the side Australia bring aren't going to be strong," Cook said.
"Anyone who thinks this is going to be a really easy series is going to be in for a huge surprise because as far as the England team is concerned there's no such thing as a weak Australia side."
The Australian top order looked especially vulnerable against spin on the sub-continent and with their own slow bowlers largely unimpressive, Cook refused to rule out preparing a string of turning wickets as his side look to beat their oldest enemy for a third straight series.
"You've got to use home advantage as best you can," he said.
"Sometimes the pitch condition is down to what the summer is like, and you can't really control the weather.
"You can try and set it up the best you can but sometimes you can overcomplicate things like that and try and get too funky. At the end of the day the side that plays the best cricket is going to win that series."
