Ministers shelved Wednesday's vote on relaxing hunting laws in England and Wales after the SNP said it would vote against the changes.
The party had previously said it would not vote on issues affecting England and Wales only.
Mr Cameron said the SNP's position was "entirely opportunistic".
Downing Street said it was "disappointing" that the vote had to be postponed, and said new proposals on the Hunting Act would be introduced "in due course".
The government has said the hunting vote will now be held after plans to give English MPs a veto on matters affecting only England - although this would not stop the hunting issue having to be voted on by the whole House of Commons.
Ms Sturgeon, Scotland's First Minister, said the decision to delay the hunting vote showed "David Cameron can't carry his own parliamentary group", and that he only had a "slender and fragile" majority.
She said he had also been forced to pull his English votes for English laws plans, showing that he was "not master of all he surveys in the House of Commons".
She said if he "had any sense", he would come back with proposals based on "fairness and reasonableness" that "work in both directions".
Earlier she had explained her party's decision to take part in the hunting vote, saying there had been "overwhelming demand" from people in England.
Another reason, she said, was because David Cameron was making Scottish MPs "second-class citizens" in the House of Commons.
Mark D'Arcy, BBC Parliamentary correspondent
With two strategic retreats in the space of a week, the intersection of Hunting and English Votes for English Laws (EVEL) is generating some really interesting politics.
Last week, the government paused its attempt to bring in EVEL, replacing a vote on Wednesday with a consultative debate.
Today another "turn your back and run away, and live to fight another day" moment on the proposed changes to the Hunting Act.
Read the blog in full
The government plans to change Commons rules to allow English, or English and Welsh, MPs a "decisive say" on legislation only applying there.
However, the current proposals would not prevent SNP MPs from voting against the changes.
Downing Street said there were no plans to change the current proposals.
This is because the statutory instrument ministers want to use to change the law would require the support of the whole of the House of Commons.
The government's decision to reschedule the vote came as anti-hunting protesters gathered at the Houses of Parliament to protest against changing the law.
The changes would have brought the Hunting Act in line with Scotland, where an unlimited number of dogs can be used to "flush out" a fox to be shot, compared to just two in England and Wales.
It's been a rollercoaster week for the old, bitter enemies on each side of this debate.
Last Wednesday - Budget day - there was quiet jubilation in hunts in England and Wales at the prospect of the loathed Hunting Act being relaxed.
Dignity would be restored: they could hunt without their every move being filmed. Animal welfare groups were devastated: it was a sneaky step, hunting would be back, and they only had a week to mobilise.
Now with the abandonment of the vote, their fortunes have apparently been reversed.
But this isn't a tale of victory and defeat. Both sides now know the government's desire to change the Hunting Act.
They are digging in for a much more protracted fight that could - believe it or not - become even more bitter.
But the 56 SNP MPs, plus Labour and some Conservative MPs opposed to hunting, meant the government's change stood little chance of being approved in Wednesday's free vote.
The SNP says it will now consider tightening the law in Scotland to match England and Wales.
Maria Eagle, Labour's shadow environment secretary, said: "David Cameron is now running scared because he knew he was going to lose the vote on fox-hunting."
Meanwhile, a poll for the BBC's Victoria Derbyshire show has suggested almost three in four British adults are against making fox hunting legal.
The poll, conducted by ComRes, asked 1,005 people if the practice "should or should not be made legal again?".
SNP leader Nicola Sturgeon has told David Cameron he is "not master of all he surveys" after her party forced a delay in a planned fox-hunting vote.