The third-place side in the cinch Premiership have suffered a blip of late, going three league games without victory and needing extra-time and penalties to defeat Livingston in the fifth round of the Scottish Cup.
Hearts have netted just once in that run as the players have felt the effect of a punishing schedule with eight games in 26 days.
Without a midweek fixture for the first time in 2022, the head coach has granted his squad two days off before Saturday’s match against St Johnstone and he believes they’ll reap the benefits from it.
“It's part of football where you go through these wee periods like that,” Neilson told the Evening News. “Like the game against Dundee we have three or four brilliant chances and we just don't take them.
“It’s a matter of freshness as well. You hesitant when you're not quite there.
“We've used the least amount of players this season of all the teams in the league. It’s a lot of games for these guys to play.
“There's going to be some fatigue in there. I've felt it in the last couple of games that they need a break there and need to come back fresh."
The Tynecastle boss has his fingers crossed for a favourable tie when the draw is made for quarter-finals tonight.
"We would like a home tie, which is the most important thing,” he said. “Hopefully we can get this place full and get it rocking to help us on our way.”