The Dons are on an unbeaten run of 10 Premiership matches that has seen them pick up one point more than Celtic during that same period, and McInnes says his players have responded brilliantly to similar pressures to those experienced by the defending champions.
He said: "There is a huge demand on this club and I said that even last season we got a wee bit of Celtic in us.
"That’s because there was a feeling from everybody, and not just our own support, for us to keep winning.
"The players have done that time and time again. We have 3,000 at away games and 15,000 at home games turning up expecting us to win.
"That’s the way it is in terms of demands for Celtic and we have created that ourselves and the players have dealt with that more often than not."
McInnes added: "We’re not perfect by any stretch but we’re always competitive and trying to be that and the importance of my good players really turning up and playing to their level is pivotal to everything we do."