The star all-rounder is currently banned from the international game while authorities probe his alleged involvement in a late-night fight outside a nightclub.
Cook, a former captain who will become the first Englishman to play 150 Tests when he appears against Australia in Thursday's crucial third Ashes clash in Perth, admits his side has been slow to learn from the fall-out.
Dubbed a "behavioural cleanskin", Cook senses England should have learnt their lesson months ago that standards would be intensely scrutinised in the wake of the Stokes scandal.
"It has been a very strange thing," he told reporters in Perth late on Tuesday.
"The world has obviously changed for the English cricket team from September. We have taken a couple of months to really realise that.
"These last two incidents have proved that. I’ve seen words written down, 'trivial misdemeanour at best', but since the Stokes incident times have changed for the English cricket team."
Cook was referring to further off-field alcohol-related scandals involving Jonny Bairstow and Ben Duckett on the tour of Australia.
"It's sad in some ways because we have always been a bit different to football and been able to go under the radar a bit and enjoy playing cricket for England and enjoy seeing the country outside that," Cook said.
But the spotlight was now firmly on England and its off-field antics and "it's now down to us to adjust to it quickly and we can’t afford any more mistakes".
Experienced fast bowler James Anderson said while the Duckett incident was not malicious and a "bit of a non-event", the tourists had to understand the current situation and act smarter.
Duckett was fined and will play no further part in the remaining matches for the England Lions in Australia after he poured a beer over Anderson in a Perth bar.
"The frustrating thing is that what was a pretty silly incident would have gone unnoticed before but now puts an unfair question mark over our (team's) culture," Anderson wrote in a column for Britain's Telegraph newspaper.
"We are all aware that from now on even a minor incident will be seized upon.
"I know Australia will use the Duckett incident as a way of goading us, or taking the mickey. Fine. The players have moved on already. Our main focus is getting back in the series. That is all everyone is talking about."
With batsman Steve Smith shaping up as Australia's danger man in Perth, Anderson said he would again try to get inside his "bubble", suggesting the Australia skipper can expect some serious sledging.
"In the first innings (in Adelaide) I sensed he was more bothered about what Stuart (Broad) and I were saying to him, which was not very interesting," Anderson said of Smith.
"As a bowler, once you get him out a couple of times you realise he is not superhuman," he added. "You realise 'I can bowl to this guy' and that makes a big difference."
First Published: December 13, 2017, 8:37 AM IST