Smith scored 144 and 142 in Australia's 251-run win against England at the Edgbaston in his comeback Test after being banned for a year due to the ball-tampering scandal.
McGrath believes that it was the hunger to succeed having lost out a year of Test cricket that was evident in his batting.
"He (Smith) just went out there and looked at ease, he looked like he had so much more time than anyone else in the whole match. That episode made him a lot hungrier. Those were couple of special innings, they meant a lot to him and the rest of the team," he added.