Ally McCoist's side maintained their unbeaten run in SPFL League 1 thanks to goals from Fraser Aird and substitute Nicky Clark, but Ian Black, the Scottish international midfielder, was carried off after a foot injury and Nicky Law was withdrawn in the first half because of a back injury.
The Rangers manager said both players would be assessed in the next 24 hours, adding: "We will keep our fingers crossed because it's not ideal."
McCoist also pointed out that scans on two previously injured players - Andy Little and David Templeton - "are not too encouraging" .
He added of Black: "He's caught the lad's [Graham Hay] foot as he's attempted to hit it. I was surprised he went for it because I couldn't see it ending in anything other than tears. The doc's looking at him at the moment and he's on the treatment table just now."
Rangers, who lost their first goal away from home since October in the league, played poorly with Ray McKinnon, the Brechin City manager, blunt about his opponents' prospects against Dundee United.
"If they play like that today, they will lose. No doubt about it because Dundee United are a really decent side going forward," said the former Tannadice full-back.
"United are young, energetic, they have good players and goalscorers in their team. It is difficult for Rangers coming to places like this and raising their game week-in, week out, I get that. But they will need to raise their game against Dundee United."
McKinnon was critical of Andrew Dallas, the match referee, and his officials. "You want a bit of parity but I don't think we got that today," he said of a match when his player, Alan Trouten, was booked for simulation as he claimed a penalty.
However, McCoist said: ' I don't think it's anything like a penalty. I think the lad takes a touch and our keeper has come out and made a good save. I don't think the boy should be booked either. I think it's a corner."
Trouten, though, said: "By the look on Cammy Bell's face, he thinks it's a penalty. There was definite contact."