The Dons were hampered by a familiar lack of creativity as supporters endured their seventh goalless draw of the season when McInnes took charge of them for the first time on Monday at Easter Road.
McInnes has vowed to balance the need to finish as high up the bottom six of the Clydesdale Bank Premier League as possible with the requirement to assess his squad ahead of a summer rebuilding job.
And, ahead of their first home match in charge against Kilmarnock, Anderson believes it could be the start of next season before McInnes and assistant Tony Docherty can truly make their mark after replacing Craig Brown and Archie Knox.
"From inside the club there have been noticeable changes," the centre-back said. "They have got their own ideas for training from what we have seen. For the supporters to see any difference, I think it might take a little bit longer for the manager to get his ideas across and for them to stick with the players.
"We will be using between now and the end of the season (to do that) and we'll start to see a difference perhaps in the way the team plays."
Several players are trying to earn new contracts, but Anderson stressed that no-one should feel safe.
"If we don't keep our eye on it, I'm sure next season might not be here for some players," the 34-year-old said.
"Everyone is really in the same boat, whether they're in contract or not. They are still trying to prove to the manager they deserve to be in the team next season.
"Even if you have a contract, if you don't impress the manager there will be plenty of players that will come in and take your place in the team. It happens every season, whether or not it was the current manager or the old manager."