Speaking at a meeting of the cross-party Petitions Committee, Huddleston was asked by Shadow Sports Minister Alison McGovern when government-backed pilots with limited numbers of spectators in attendance may resume.
Plans for a partial and staged return of fans from 1 October were suspended after a rise in the number of coronavirus cases.
However, at the same time London’s O2 Arena announced 4,700 people would be able to attend a concert in December.
The Royal Albert Hall will also welcome audiences of up to 2,500 back for a number of concerts this Christmas with one senior source from within football telling BBC Sport: “The inconsistency in the approach is stark and illogical.”
McGovern said: “I worry that (sports) have been left hanging a bit.
“The position that football has been put in compared to other large events is hard to understand.
“We were on a journey and the process needs to be completed. So can he say when he anticipates that happening?”
Huddleston replied: “We want to get pilots back and fans back into stadia as soon as possible.
“We’ve had a plan from very early on in lockdown. And it’s been stated and it’s out there, and what we’ve had to do on a couple of occasions unfortunately is press the pause button. But we want to get back to the plan as soon as we can.”
Last month the English Football League rejected a £50m bail-out offer from the Premier League. The heads of both organisations, along with the chairman of the Football Association, will appear in front of the Digital, Culture, Media and Sport committee on Tuesday.
“There is plenty of money in football, but it’s not distributed in the right way,” said Huddleston.
“For the good of the sport, they must come to an arrangement. It’s not acceptable for public money to be bailing out elite football.
“I do recognise they each have stakeholders who are difficult to deal with but I do appeal to them to come to a compromise as soon as possible.”
The minister said the DCMS was in the “final stages” of discussions with the Treasury over a rescue package for other sports facing an unprecedented financial crisis because of the pandemic.