Khan, who is now in Mohali, Punjab, for the second Test against Australia, claimed that the Australians lacked the firepower to retain the Border-Gavaskar Trophy.
Zaheer, man of the match in the drawn Test with six wickets and a half-century, declared the pressure was on Australia to quickly find an answer or the series would be lost.
The tourists were in control of the Bangalore opener until a first-innings eighth-wicket stand of 80 between Harbhajan Singh and Zaheer late on day three shifted the momentum, with Australia never really recovering.
Buoyed by surviving 73 overs on day five for the loss of just four wickets, India cannot wait for the second Test in Mohali, starting Friday.
"We know that they can't take 20 wickets and they are on the back foot. They couldn't get me and Bhaji out. We are in with a big chance. They are under pressure. We know that," the Daily Telegraph quoted him, as saying.
Zaheer had a crack at the Australians in a press conference and earlier on the field when he accepted his individual award.
It was there he also claimed the tourists had been too defensive in the Test, earning a rebuke from Australian captain Ricky Ponting.
"He can have a bit of a chuckle to himself, I don't think it means too much to us," Ponting said.
"This match clearly shows that," he said. "On a fifth-day wicket, the spinners couldn''t do us any harm. So that tells everyone what their spin attack is all about. And even the pacers didn''t look like getting a wicket at any stage. The pressure is on them to take 20 wickets," Zaheer said.