A trip to Pittodrie in January was the reward handed to Stenny after last week's dramatic third round win over neighbours Falkirk.
And McMenamin believes the glamour tie will help keep everyone on their toes between now and then.
He said: ""They've got a target now for this Aberdeen game when they're all going to want to be involve and if they are going to be involved they're going to have to their consistency levels reasonably high and out themselves in a position where they can't get dropped.
"It's a good thing all round - the result, the draw and hopefully now we can get a bit of momentum to climb up the league.
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"It's a great draw for the club against one of the top teams in Scotland. Since I joined the club four or five years ago we've never really had a real good away tie."
But there's plenty of football for the Warriors to play between now and then, starting with Saturday's trip to an Arbroath side protecting one of only four unbeaten league records in Britain, along with Manchester City, Liverpool and Inverness Caley Thistle.
McMenamin said: "It's going to be a very tough game but it's a game that we're looking forward to.
"I said to them after the game on Saturday that it's time to kick on now.
"They've set a standard which is very high and it's not going to be easy, but they've proved they can play at that level and it's something they need to do consistently if they're going to start climbing the league.
"We should be riding high so we'll go up there with a lot of confidence and a game plan that I hope will get us something."