For the first time this season, Rangers recorded three consecutive Premiership victories when they followed up their back-to-back wins over Aberdeen with last Saturday’s 2-1 home success against Ross County.
It has sparked some chatter among the more optimistic elements of the Ibrox club’s support that catching champions Celtic, who are currently five points ahead of Rangers with a game in hand, may yet be possible.
But, while Murty insists he will never seek to limit their ambitions, he is more concerned with avoiding a repeat of the unexpected defeats Rangers suffered on his watch against Hamilton and Dundee last month.
The 43-year-old, who will remain in charge until the end of the year after Derek McInnes last week turned down the chance to become Rangers manager, now faces a testing spell of five league games in 18 days before the winter break.
Starting against Hibs at Easter Road tonight, the sequence is followed by meetings with St Johnstone, Kilmarnock and Motherwell before a trip to Celtic Park on 30 December.
“At the moment Celtic are on top and we are chasing,” said Murty. “Chasing is a good position to be in, but we have to be better and more consistent – that’s the theme throughout the season.
“We have had a couple of good results, but then possibly had a stumble and we have to hit a level of consistency and performance that we have shown we can do, but we have to do it more often if we are going to get back towards the top of the table.
“We are in second at the moment, but we have to take care of the small details and see where we are then.
“This is Rangers, we should be looking at trying to stay unbeaten through this run of games anyway. But we are looking at making sure we take care of one marker at a time. If we get carried away and start looking ahead to the game at Celtic Park, I have got no doubt there are opponents before that that will be looking to trip us up.
“Hibs will be looking to go and win the game and we have to deal with that, their intensity, their level, their play, because they have got some good players. They have been successful this season and we have to make sure we are fully prepared for that. Then, if we get closer to Celtic, great. But let’s make sure we focus on our process and our game first. Let’s not worry about Celtic, let’s concern ourselves with us.
“I’m not one for limits personally, I’m not one for setting ceilings on players. I think you should aspire to be at the very top, you should always aim for that and see where it takes you.
“The players have been criticised this season, the board have been criticised, the club has been criticised, the fans have been criticised – and we are in second place.
“So if we can take all that on board and still ride it out and be in second place, then we can actually push on. We can deal with it and move forward and still be capable of getting positive results. If the players believe that I think that’s half the battle.”
Murty, pictured, was at Easter Road on Sunday to watch Hibs draw 2-2 with Celtic but believes his spy mission may have offered him very little in the way of valuable intelligence ahead of Rangers’ visit this evening.
“I actually questioned how useful it was because I am not sure that Hibs will play in the same manner against us,” he said. “I think they will have a different mindset. But it was useful for me to see the environment and to see some of their personnel without being constrained by the TV screen, to see how they move and what their strengths are. Then we came back and watched three or four hours of their other games and seeing them play in different formations. Neil Lennon is very adept at changing formations within the game too and we have to be on our toes dealing with that.
“The target is to go and win and make sure we do ourselves justice. We can’t control that Celtic went there and picked up a point. We are going there to hopefully keep a clean sheet and get at least one point but we would like to get three.
“We have to make sure we deliver a level of intensity we didn’t against Ross County, although we managed to get the win. We have shown that we can go to challenging environments and get wins by making sure we play positively, on the front foot. We have quality, players that can go and hurt opponents and we have to make sure we don’t shoot ourselves in the foot from the start and that we stay in the game together for as long as we can and then hopefully we get opportunities.”