The two Yorkshire clubs were both without a game on Boxing Day due to their scheduled fixtures falling victim to the heavy rain that left the north saturated.
Adding to the sense of frustration felt at Valley Parade and Bramall Lane was the fact all five of the clubs above Bradford and the Blades in the table went on to claim three points to steal a march on the duo.
It means Parkinson’s side trail the top six by three points, albeit with at least one game in hand on all those teams above them in the table. United, meanwhile, are a point adrift of the Bantams in ninth place.
In the bigger picture, Walsall, Burton Albion, Gillingham and Coventry City are separated by just two points, but the Sky Blues are a further six clear of nearest challengers Peterborough in fifth.
This suggests the scrap for automatic promotion could be between this leading quartet.
Parkinson, however, believes it is far too early in the season for this to be the case.
“Bramall Lane is one of the bigger stages in League One and we are expecting a really good atmosphere,” said the Bantams’ chief, who was a major target of the Blades last summer before the South Yorkshire club opted to bring in Nigel Adkins.
“You look at their squad and it is as good a squad as there is in League One. But there are a lot of good teams in League One and that is why nothing can be discounted.
“We are not yet at the halfway stage in our season and so many teams in the mix. There are surprise results all the time, too.
“This league is so open. Obviously, Burton have been the surprise package, but everyone is in the mix. People may look at the top few teams, but so many teams are capable of forcing their way into the reckoning. It is going to be a very, very exciting season.”
Ahead of the festive programme – which suffered a false start for United due to their postponed trip to Wigan Athletic – Adkins insisted a place in the top two was still within grasp for his side. “So long as you are in the hunt come January then it gives you something to build on in the second half (of the season),” said the Blades’ chief, who has won promotion from this level three times in his managerial career.
“We were lower at Southampton, we weren’t in the top two or anywhere near it when we went in there. But we got up.
“Bradford, though, will be tough. We had a real battle at their place earlier this season and I am expecting the same again.”
As for City, just one defeat in 11 league outings has raised hopes of a tilt at promotion in the new year. Around 3,500 fans are expected to make the trip to Bramall Lane from West Yorkshire and Parkinson is adamant his players must reward that travelling support.
He added: “Sheffield United will be a big occasion for both teams.
“At any point in a season, going to Bramall Lane is terrific but at Christmas with a big crowd expected then it is something to really relish.”
Elsewhere in League One, Barnsley – also without a game on Boxing Day due to the weather – host Blackpool and Doncaster Rovers travel to Oldham determined to bounce back from the disappointing 1-0 festive defeat at home to Scunthorpe United.
In the Championship, Hull City travel to Preston knowing victory will mean moving into the top two – albeit possibly for only a couple of hours due to Middlesbrough being in action at tea-time against Sheffield Wednesday.
Robert Snodgrass is expected to start for the Tigers, as manager Steve Bruce considers changes despite his side’s 3-0 win at home to Burnley.
Bruce said: “I have been in it a long time and it would be easy to just play the same team.
“But some don’t recover. Abel (Hernandez) is one where there is a big question mark over whether he can have the same impact.
“Statistics tell me he struggles to follow it up when he plays games so quickly.
“Whereas Sam Clucas, for example, could play the day after a game, no problem. Hernandez, though, struggles to recover.”