Top scorer Boyd and influential midfielder Davis limped off with groin and thigh problems respectively, the extent of which will be assessed by the club's medical staff over the next 24 hours.
Rangers recovered from a 3-2 half-time deficit at New Douglas Park to force a replay at Ibrox on 19 January and remain in contention to win all three domestic trophies. But with financial circumstances preventing them from adding to their squad, they can ill afford lengthy absences for Boyd and Davis. The quartet of Pedro Mendes, Nacho Novo, Steven Naismith and DaMarcus Beasley are already injured, while Madjid Bougherra will be absent for the rest of the month on Africa Cup of Nations duty. Lee McCulloch and Kenny Miller are also suspended for next Saturday's return to New Douglas Park on SPL business.
"I would be lying if I said it isn't something we are worried about," said Rangers assistant manager McCoist. "It is an obvious concern. Injuries are part and parcel of football, but we are pretty sparse in terms of players at the moment and could have done without losing Kris and Steven.
"We will know over the next day or two how serious their injuries are and we just have to hope they won't be out for long. Kris has been struggling with a groin problem for a few weeks, while Steven suffered a dead leg. Our squad is certainly going to be put to the test in the coming weeks and we have to handle it."
McCoist was simply relieved Rangers had kept their grip on the Scottish Cup yesterday after watching a 2-0 lead wiped out by three goals from Hamilton in the closing stages of the first half. Kenny Miller converted a controversially awarded penalty kick in the second half to take the tie back to Ibrox where a fifth-round trip to St Mirren will be on the line.
"The first half was a bit bizarre," added McCoist, "because we went 2-0 up without having played well. Our second goal was a marvellous goal, but it was the best bit of football we played and I wasn't quite sure how we got to being 2-0 ahead.
"At the same time, I didn't see Hamilton scoring three goals in the last ten minutes of the first half. The goals we lost were poor. We asked the team a few questions at half-time and, without playing great, they were certainly a lot better in the second half. Hamilton have shown great spirit and we told our lads they had to equal it. I think both teams probably deserve another crack at it."
Rangers striker Miller, who maintained his recent hot streak of scoring form with yet another double, conceded that he feared the worst when Hamilton overturned their 2-0 deficit.
"You do start to think it was maybe written in the stars for them to win the tie when it happens like that," said Miller. "When we go 2-0 up against anyone, we should be seeing it out. We know it wasn't good enough and in the end we are happy to get them back to Ibrox."
Hamilton were left to rue referee Charlie Richmond's decision to penalise Stuart Elliott for handball in awarding Rangers the penalty from which Miller made it 3-3.
Former Northern Ireland international Elliott, who was making his debut for Accies, said: "I thought the decision was very soft. I was on the ground and there was nothing I could do about it. It certainly wasn't intentional and I was trying to get my hand out of the way. It's disappointing, because I felt we were the better side."
Hamilton manager Billy Reid was more philosophical about the penalty decision, perhaps mindful that the spot-kick awarded to his own team for Kirk Broadfoot's challenge on Mark McLaughlin was also debatable.
"I don't have a problem with it," said Reid. "The ref has a decision to make and we stand by it. The first half was crazy, because we played well yet found ourselves 2-0 down. We almost completely dominated the game in the first half and deserved to get back into it. Rangers came out stronger in the second half but didn't cause us too many problems. I think our lack of games recently maybe had an effect on us as the second half went on.
"The players are gutted. They did enough to win the game over the 90 minutes and you don't get too many chances to do that against the Old Firm clubs. A lot will be made of Rangers not playing well, but that would discredit Hamilton."