The Three Lions head into a crucial double-header on Friday, when they tackle Group H minnows San Marino.
Whilst victory in Serravalle is taken for granted, rather more onerous is the trip to Montenegro that follows.
For the eastern Europeans are already two points clear of Hodgson's men, and did not lose either match against England during the Euro 2012 qualifying programme.
Defeat would be unthinkable. But Parker is refusing to look on the bleak side.
"I am not really worried," he said.
"You can't go in with that mentality. That is when you have doubts and start worrying. Stress hits and you don't do the things that normally come naturally.
"We have got a good enough squad to qualify for the World Cup and we are in a good enough position in the group with some home games coming up."
Nevertheless, there are concerns, chiefly revolving around central defence given the number of withdrawals.
Parker believes Hodgson will come up with the right answers though, having been impressed at the continued positive impact of the 65-year-old and the relaxed nature of his regime compared to predecessor Fabio Capello.
"Roy's man-management skills are very good," said Parker.
"He's very intense but at the same time relaxed.
"It is a lot warmer around the camp now, whether that is the culture or the language there is more of an understanding.
"He is very easy to get on with and he understands what the players want."
And Parker knows Hodgson will be basing any of his selections on age.
Now 32, the Tottenham midfielder is one of a group of experienced players some would now be looking to pension off.
Skipper Steven Gerrard, Frank Lampard and Ashley Cole are over 30. Joleon Lescott and Michael Carrick are also in the same club, and Ben Foster will be at the beginning of next month.
Yet Parker insists there is no need for concern.
The Tottenham midfielder watched 39-year-old Ryan Giggs produce a virtuoso performance against Real Madrid a couple of weeks ago.
And he believes that provided all the proof needed to ignore those pesky dates of birth.
"I don't get the age one really," he said.
"People are too hell-bent on age, whether it's bringing players through or others being too old.
"If someone is good enough and playing at their best, you pick them.
"Maybe its because I am 32, but I saw Ryan Giggs playing against Real Madrid in the Champions League. He was doing more running than anyone else.
"I don't buy into the debate at all."