Speaking during his post-match press conference after Saturday's 1-0 defeat to Barnsley at Oakwell, the Blues chief demanded that the Football League (EFL) looks into the number of "unfair" postponements his side's relegation rivals have been granted.
Karanka suggested that the South Yorkshire club, who sit three points behind Birmingham in the Championship standings but boast three game in hand, will end up fulfilling their outstanding fixtures at a stage of the season where some of their scheduled opponents may have little or nothing to play for.
The Spaniard's comments came after Rotherham's trip to title-chasing Brentford became their third match of 2020/21 to be rearranged due to a Covid-19-related issue. The clash will now take place on April 27.
“This is another thing that is curious. Those three games in hand, the second time I think they have postponed games for the covid situation,” Karanka said.
"They're going to play the games maybe when the other teams know their positions and it isn’t going to be the same.
"For example, we played them after seven or eight games, they are going to play the games when they are rested. They are going to play against Brentford, maybe they are in the Premier League or they are already in the play-off positions.
“It is something the EFL need to check because I don’t think it is normal, it is unfair. Our club hasn’t had one game postponed because we are looking after ourselves.
“It is not the first time that Rotherham is having the same problem. When you are making one mistake, maybe, but the second one I think, for me, it is not fair."
In addition to Saturday's showdown with Brentford having to be called off due to positive Covid-19 test results within the Rotherham camp, Tuesday night's game against Luton Town has also been postponed.
Before Christmas, confirmed coronavirus cases at the New York Stadium led to fixtures with Derby County and Middlesbrough being rearranged.
The Millers have also seen a number of matches lost to the weather and now face rather a hectic end to the season, with 14 of their 38 league games still to be completed.