Graeme had a baptism of fire in Scotland's opening game of the tour when he struggled with the speed and intensity against an international standard Queensland back division.
Since then, the 21-year-old has knuckled down and his performances against NSW Country last week and particularly the NSW Waratahs yesterday have left him within touching distance of a first Test cap.
"The first game against Queensland was quite an eye-opener for myself," he said.
"I saw players that I aspire to and they were just in cruise mode against us. I realised I have got a lot more work to do to get to where I want to be.
"Since that game I have looked inside myself and just tried to show I really wanted it and things came right.
"There is a lot of competition in the centres. When Tom Philip went home injured I thought there could be an opening in the Test team for me somewhere but I knew I had to work harder. I didn't want to assume anything."
Graeme will stay with the 30-man squad and begin preparations for the first Test against the Wallabies in Melbourne, with coach Matt Williams set to announce his match XXII on Thursday.
While Williams was uncharacteristically brutal in his condemnation of yesterday's 33-15 defeat, he reserved hearty praise for Graeme and indicated the Glasgow centre is ready for the step up to Test rugby.
"That game was worth it if only for Graeme Morrison's performance. He was absolutely outstanding, the best player on the field," he said.
Williams felt Graeme was "not out of his depth" facing Australia international Nathan Grey, who was equally as impressed with the uncapped Glasgow centre.
"I have still got a lot of work to do, it has not gone to my head. When we perform that badly I am not going to take any credit for my own performance," he said.
"I just don't think the frame of mind was quite as it should have been.
"I don't know whether things were complacent? We had a good result against NSW Country and we came to play against a weakened Waratahs side, so whether or not that affected some of the boys I don't know."