The midfielder revealed that there was a lot of anger amongst the squad following Saturday's performance.
A late equaliser from Martyn Waghorn spared some of the Gers' blushes against the Ton, but Halliday explained that it did not prevent the fiery exchange that occurred after the game (via Daily Record).
"It was an angry and frustrated dressing-room at full time," he revealed. "We had to get a few things out in the air. Things had to be said.
"The players do most of the talking in situations like that. The gaffer wants to hear the thoughts from the boys and then he'll step in if something needs to be said. A few things came out but we need to go again because we're still three points clear at the top.
"We've two massive games coming up and I think we'll get the job done. We've cleared the air and we go again on Monday."
Despite Mark Warburton's side slipping up, and losing their perfect home record in the process, Rangers' lead at the top of the Scottish Championship was not hindered as Hibernian also needed a late equaliser to get a point from third-placed Falkirk.
Nevertheless, the draw at Ibrox was the third time in their last five league games that the Gers have dropped points, perhaps hinting that the squad are starting to become slightly complacent, and are assuming that automatic promotion to the Premiership is assured.
However, their fighting spirit - that was evident on, and possibly off, the pitch on Saturday - suggests that they have come to the realisation that they are not going to be allowed to limp over the line, and thus need to find the ruthless form that saw them fly out of the blocks at the start of the campaign.