But the midfielder will view St Johnstone's season as a failure if they are not challenging in the top six come the end of the campaign.
McInnes has made an early impact at Pittodrie, although the Dons are looking to bounce back from their 2-1 defeat by Hearts last weekend when they host Saints on Saturday.
And Millar feels his thorough approach will pay dividends.
The 30-year-old, who is now in his sixth season at McDiarmid Park, said: "He had a big impact on my career. He brought me here from Morton and developed me. I have felt since I came here I have always improved.
"He gave me a chance to play SPL football and his attention to detail and work ethos is something I have taken from him. We still keep in contact and he is good for advice.
"Derek has always been very thorough in his preparation on and off the park, with sports science, analysis and different ways to improve. Sometimes it's the wee things, a tweak here and a tweak there, that can make things better.
"If they continue going the way they are, Aberdeen are a fantastically-supported club, it's good for the Scottish game to have a strong Aberdeen side competing in the league.
"They have a strong squad and they they have been rightly tipped to be challenging for second or third place this year."
St Johnstone have no fresh injuries for the clash but goalkeeper Alan Mannus remains out with a shoulder injury.
And midfielder David Robertson is set for some Under-20s action next week as he continues his return from a broken leg. Aberdeen winger Peter Pawlett insists he is not a diver - and that his "natural" way of falling is working against him.
Pawlett was booked for simulation by Alan Muir during Aberdeen's 2-1 defeat by Hearts last weekend despite appearing to be caught by Jamie Walker's sliding challenge just inside the box.
But it is not the first time the 22-year-old has been cautioned in such fashion. He received his second two-match ban for simulation from a Scottish Football Association panel in May over the penalty incident that sealed Dundee's relegation.
Pawlett was also booked for diving twice in a month earlier this year. However, he argued he cannot easily change the way he goes down.
Pawlett said: "I think I was unfortunate against Hearts, I think TV evidence clearly showed I was clipped. "I think the way I go down doesn't help the ref's decision but that's the natural way I go down. I'm not diving, I've done that ever since I was a kid.
"I know when people look at it, and I sometimes look at it and think: 'What am I doing?' But at the time it's natural and I am not putting anything on.
"The physio said to me: 'You need to change the way you go down'. But that would be diving.
"It's difficult, especially when you are going at such a speed, to think about the way you are going to go down."
Aberdeen have lost three players for the clash. Midfielder Willo Flood (hamstring), forward Josh Magennis (shoulder) and winger Jonny Hayes (concussion) all drop out of the squad.
Midfielders Barry Robson and Chris Clark remain on the sidelines for Saturday's match as they continue to recover from knee injuries.
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