May departed for Sky Bet Championship side Sheffield Wednesday in a £800,000 transfer in the close season. However, McInnes is adamant that there will be others ready to step into the spotlight for St Johnstone when his side visit McDiarmid Park today.
"I think it is disrespectful to say they won't cope without him," said the Aberdeen manager. "There is no doubt that they will miss him as he scored 27 goals last season and I am sure Tommy [Wright, the St Johnstone manager] would say the same. I am sure Stevie would have gone on to show more of that again this season had he still been there.
"You can't say he won't be missed but I am sure they will find ways to cope and get on with it. Somebody else will maybe take the opportunity and rise to it. They have too many good players at St Johnstone to have one player impact on their season. I am sure they will be there or thereabouts at the top end of the table come the end of the season, just as they have been for the last few seasons."
McInnes, who will have Russell Anderson available again after the club captain missed the win at Kilmarnock 10 days ago, praised his former club for how well they are run. Indeed, he can understand fully why the Perth side have been so careful with the money received for May, with Simon Lappin the only player to have been added to the squad since then. The former Norwich City and Cardiff City midfielder arrived on a two-year contract this week.
"They know exactly what they are doing there," said McInnes. "From the current chairman Steve Brown to his dad, Geoff, they know the parameters they need to work within. They are a great success story and the last few seasons have been a really good period for the club.
"They are a really well-established Scottish Premiership team now. Winning the Scottish Cup last season was fantastic for them. There is a familiarity and stability about St Johnstone. They have proven to be a really tough side to play against in the last while.
"We won 2-0 at McDiarmid Park last year but it was a tight, competitive game and it took two bits of quality from Niall McGinn and Peter Pawlett to win the game. We will probably need to see similar qualities on show for us to win [today]."
However, McInnes will be without Jeff Monakana this afternoon - the winger, on loan from Brighton & Hove Albion, has contracted an infection in his back - did not rule out the prospect of adding to his squad before the transfer window closes.
"You would never say never because we still have a couple of games to get through before the window closes," he added. "Injuries can still impact on what you do. We are still hoping nobody comes knocking for our players as well."
Lappin, at least, answered Wright when he came calling this week. The 31-year-old started his career with St Mirren and spent time on loan at Motherwell in 2008. He admitted that it did not take too much to persuade him to return to Scotland and sign for St Johnstone.
"I'm absolutely thrilled," said the midfielder, who also had an option to join Major League Soccer in the United States. "The club has been going well, with the success they had last season. And I am delighted to be a part of that and grateful to the manager for giving me the opportunity to come to a fantastic club.
"I have known him from a few years back when he was goalkeeping coach at Norwich, and when I spoke to him a few weeks ago he didn't have to sell the club too much to me. I'm delighted to be here and I'm thoroughly looking forward to the season ahead."
Wright hopes to benefit from another old acquaintance in the coming weeks too, having invited Manchester City great Shaun Goater - a former team-mate at Maine Road - to spend time working with the St Johnstone strikers. "I called him up a few weeks ago and he invited me to Perth," said Goater, who is eager to get into coaching.
"I've been going round visiting a lot of old team-mates. While I'm up here Tommy said I could do a little bit with the St Johnstone strikers - that was something I was excited about."