After being drawn against Championship rivals in the previous two rounds, the Whites have been handed a clash against Premier League opposition following their victory over Bolton on Saturday.
And while Evans admitted that it will be an uphill battle if they hope to pull off a shock, he insisted that they can secure a place in the quarter-finals.
"We're the only lower placed team away from home, we've not landed any of the big names and we're not at Elland Road so those are the downsides," he said, as reported by the Yorkshire Evening Post.
"But on the upside it's a game we can win.
"We'll take thousands upon thousands of supporters with us and we'll turn it into a proper cup tie. We have to turn it into a cup tie."
While the Hornets have been mightily impressive since their promotion to the top flight, Quique Sanchez Flores will be aware that some sides who have enjoyed excellent starts to the campaign in the past have then gone on a rotten run that has seen them dragged into a relegation scrap.
And while February's tie will surely come too soon for Flores to become that concerned about any slide down the table - even if they were to lose all three of their games before United's visit - having admitted that it will be a big ask for Leeds to book a place in the sixth round, Evans will be hoping that other priorities result in Watford taking the FA Cup a little less seriously as it may leave the door open for the Whites to spring a surprise.