Peterhead finished the season just two points behind Ayr, but McInally reckons the Somerset Park club are a much bigger outfit than the Blue Toon and will be under greater pressure to succeed.
McInally said: “We will not be expected to knock Ayr out, but we will give it a go.
“They are a much bigger club than Peterhead and being involved in the chase for promotion is expected of them whereas, for us, we can enjoy the adventure.”
Peterhead have Rory McAllister suspended, although the striker will be available for the return leg on Saturday. As well as McAllister, Peterhead will be without injured Ally Gilchrist and Jamie Stevenson while Scott Ross is also doubtful.
Meanwhile, Ayr manager Ian McCall is confident his side will be ready for Peterhead despite losing 3-0 to Airdie on Saturday.
McCall said: “I tried a few things out at the weekend but they did not all work. We will be ready to face a good Peterhead side and a side that have shown they are not a one man team in the absence of Rory McAllister. “
Peter Murphy returns from suspension, with only Jamie Adams unavailable to McCall.