Moeen, 27, took 19 wickets in five Tests against India in 2014 but was less impressive in last week's win over West Indies, despite figures of 4-98.
"India didn't show me enough respect in the way they batted against me," he said. "It's going to be tougher playing New Zealand and Australia."
England start five Tests against the Kiwis in May and Australia in July.
In less than a year since making his Test debut against Sri Lanka, Worcestershire's Moeen has become key to England's attack and was flown out to Grenada for the victory over West Indies in the second Test after recovering from a side strain.
The off-spinner says that decision by the selectors gave him confidence and, despite a slow start with first innings figures of 1-47 then took three tail-end wickets as England bowled the hosts out for 307 in their second innings.
"Even when I wasn't bowling so well in the first innings it gave me confidence the management backed me, liked the way I bowl and think I'm a threat to the batsmen," added Moeen, who averages 27.53 with the ball in his eight Tests.
After a century in his second Test outing, Moeen has not contributed more than 40 in any knock since and is seen as an option to bat at six, with Jos Butler and Ben Stokes also possibilities.
"Whatever the captain and coach want me to bat I'm more than happy," he said. "We see it as a strong batting line up. Hopefully when we all play games and click we can be dangerous."
England begin their final Test of their tour of West Indies on 1 May, leading 1-0 in the series.

In May, Mr Joyce vowed to press charges against a man who struck him with a pie over his support for same-sex marriage, which is not legal in Australia.
Mr Joyce has also faced criticism from some politicians who say he should not take a political stance on behalf of the airline.
However, he said his company "would be active out there" in campaigning.
"I believe we have to get behind it and make sure that we have a 'yes' vote and certainly I will be out there strongly campaigning for a 'yes' vote," he said.
"We believe the social issues are very important of all of your [company] stakeholders and are very important for this country."
Australians will be asked their views on same-sex marriage through a voluntary, non-binding ballot to begin next month.
If it shows support for changing Australia's Marriage Act, it is expected that a vote in parliament will follow. However, MPs would not be bound to vote in line with the public.
Mr Joyce was one of 20 company chief executives who signed a petition in March calling on Prime Minister Malcolm Turnbull to legalise same-sex marriage.
It led to criticism by Immigration Minister Peter Dutton, who said it was "unacceptable that people would use companies and the money of publicly-listed companies to throw their weight around".
"If Alan Joyce and any other CEO wants to campaign on this or any other issue in their own time and on their own dime, good luck to them," Mr Dutton said at the time.
Two months later, Mr Joyce was giving a speech in Perth when an intruder shoved him in the face with a meringue pie.
"From my reading, it would appear that Alan Joyce is very much part of a network trying to subvert the federal parliamentary process around the issue of marriage equality," the intruder, Tony Overheu, told the Australian Broadcasting Corp.
Mr Joyce later said he would press charges against Mr Overheu.
Polls in recent years have shown a majority of Australians support same-sex marriage.
England spinner Moeen Ali expects his second summer of Test cricket to prove more difficult than his first.
[NEXT_CONCEPT]
Qantas chief executive Alan Joyce has urged Australians to support same-sex marriage in a looming postal vote.