The three-test series against Pakistan, for which they leave this week, takes place in the UAE, where England were beaten 3-0 in 2012 and where Pakistan have never lost a series.
Then they travel to South Africa for a four-test series.
Cook said the players were in great heart after beating Australia 3-2 in England to regain the Ashes but that there is little time these days in international cricket to sit back and enjoy success.
"It's been a brilliant couple of weeks off after you win such a big series but it's amazing how quickly it has come round again," he told Sky Sports News.
"There is no rest and the guys have to park the Ashes and start looking forward.
"Winning away from home in international cricket is not done very often at the moment."
He believes that will be particularly hard in the UAE, although "it's a brilliant place to play cricket because it's so unique".
Cook would give few clues about who might fill the troublesome opening batsman's slot alongside him in either series, for which Alex Hales and spinner Moeen Ali are seen as the main contenders.
"We have to be flexible," he said. "We might have to have a short-term option. It might be that Mo opens the batting in this series and not in South Africa or that Alex takes his chance in a warm-up game.
"So we have options and we have to be clear pretty early on what we're going to do.
"It's a pretty tough job, (opening), you're playing against the best bowlers in the world who are fresh, with the new ball. And it's a big step from county cricket to international cricket."
England arrive in the UAE this week and start the first test on Oct.13. After the three tests, there are four ODIs and three T20 internationals before the end of November.
(Reporting by Steve Tongue; editing by Martyn Herman)
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