Murty was handed the reins less than 48 hours before Sunday’s William Hill Scottish Cup visit of Morton and led the team to a 2-1 fifth-round victory.
The former Scotland international has thanked his players for their co-operation following Mark Warburton’s shock departure.
But the Rangers Under-20s coach has left them in no doubt that he wants a major improvement in performance for Sunday’s Ladbrokes Premiership encounter with Dundee at Dens Park.
Murty told the club’s official website: “I was pleased with their attitude, I was pleased with the way they handled themselves because it is not easy and your head is all over the place.
“It is difficult to try and please a new manager, even though consciously you’re not doing it you’re just playing the game, but subconsciously you are always looking at: ‘What does he want? What is he after?’
“But I thought they got past that bit and got past a really challenging start when we conceded the goal and I have just shown them in analysis that there were some really good bits of play, we just didn’t sustain it.
“The difference between our good bits and where we want to improve are a bit stark at the moment, well they were on Sunday.”
The 42-year-old added: “I have come away from the analysis with a really positive outlook on it and I hope they have as well.
“We have sat down and the thing I have really enjoyed the most was the players’ engagement, they have really been honest and open and really engaged with what we have done. I want to thank them because it has made my transition a bit easier.”