The incident, with Anderson claiming the Rangers defender punched him in the midriff, has resulted in Kiernan being offered a two-match ban after it was highlighted by BT Sport pundit Stephen Craigan.
Rangers manager Warburton appears unhappy that Craigan pushed for a sanction against Kiernan when, as Motherwell coach, it will be a Scottish Cup tie against the Lanarkshire side at Ibrox on 21 January and then a league encounter between the same teams at Fir Park a week later that Kiernan will miss should the suspension stand.
“I’m disappointed, in terms of coverage,” Warburton said. “Coverage and conflict of interest, for me. That is my own personal view. That’s my view. It doesn’t sit right with me. To have criticism of that level, and the impact it could potentially have, it is a conflict of interest and something that has to be better.”
Warburton was speaking after watching his side lose 2-1 to Celtic at Ibrox having led the match 1-0.
The hosts could have snatched a point late on, Rangers goalscorer Kenny Miller presented with another golden chance after being picked out at the back post by Andy Halliday.
But the 37-year-old fluffed his finish and watched in horror as the ball came back off the post.
“We had chances,” conceded Warburton. “But you’ve got to take them. So we have to learn from this. The boys have got a well-deserved break now to recharge the batteries and we need to come back for a very strong second half of the season.
“I’m not worried [about Celtic’s lead]. My only focus is on Rangers. We want to take this club as high as we possibly can, get European football and kick on again.
“I’m not going to sit and say it was great that we got closer. We lost.
“I hope the fans stick with us. We are second in the table, just got promoted last year and we are second but of course we want to go higher. They have been magnificent and the support today was first class.
“And you saw after the 15, 20 minutes we were under the cosh, the crowd united then and had a reaction from the players. The support we received was excellent.”