The Bucks host National League side Gateshead, who this week appointed former Newcastle United and Everton star Steve Watson as their new manager and lie16th in the league.
And McIntosh, who has previously seen Buxton exit at this stage twice - both 1-0 defeats away at Guiseley and AFC Fylde - is hoping to cause an upset.
He said: “It’s a huge task but we just need to be competitive, be at it from the start and enjoy the occasion.
“We can’t make it easy for Gateshead. We’re at home and in front of what will hopefully be a big crowd and given our previous two attempts at this stage were away from home, this could be seen as our best ever chance to get to the first round and a potential money-spinner.
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“Steve Watson has gone in this week and he’ll be familiar with our setup having been here a couple of times with Macclesfield for pre-season games when he was coach there, so he’ll have an idea what to expect and will want to get off to a good start.
“We just have to make sure they know they’re in a tough game and the longer we can keep them within reach of a result the more we can unsettle them.”
McIntosh was speaking after seeing his side lose 2-0 at table-toppers Shaw Lane on Monday night, just 48 hours after Buxton beat Marine 2-1 (see page 55)
He said: “I’ve no complaints over the result on Monday to be honest. It wasn’t the worst we’ve played this season but we weren’t great against a side that is in great form and that I think will stay towards the top all season.
“They were a bit over-physical and the ref perhaps needed to protect us a bit better, but somehow we got away injury-free.
“We’re still in good form on the whole and have every reason to go into Saturday’s game believing we can win it.”