Rovers will look finally to get their first home win of the season when their old rivals arrive at Post Office Road.
While they were slipping to a 24-8 defeat to London Broncos on Good Friday, Sheffield were resting, having won 26-4 at Doncaster last Wednesday.
“I am not happy with how the league allowed Sheffield to play Wednesday and we had to play Friday,” said Hay, whose side sit sixth, four points behind third-placed Eagles.
“They are supposed to be Easter fixtures and I’ve not heard of an Easter Wednesday.
“We are behind the eight-ball a little bit with preparation. We’ve a lot of work to do in a short space of time. Psychologically, the players are going to be battered and they’ve got to get up for the game on Monday. There are obviously going to be changes and they have got to handle that as well.”
Andy Ellis, James Mendeika, who has not played this term due to major knee surgery, and Gareth Moore are all fit and could feature after missing the London game while former Australia and Samoa international Reni Maitua might debut after finally arriving in the country on Saturday.
Although Featherstone won their first ‘home’ match against Hunslet Hawks, that was played at Wakefield Trinity due to pitch problems, and they have subsequently lost against the competition’s big three of Bradford Bulls, Leigh Centurions and London.
Such setbacks have hurt their hopes of a top-four finish and Hay admitted: “It’s going to be a big game on Monday.
“I always thought Sheffield was going to be a bigger game than London and it definitely is now.”
The clubs, who featured in three successive Grand Finals between 2011 and 2013 with Sheffield winning the last two, are each hopeful of working their way up into Super League this term.
However, Hay conceded his side will not achieve that if there is a repeat of Friday’s no-show.
“The whole performance from start to finish was pretty embarrassing,” he said.
“The first half was bad and the second half was probably even worse. Our completion rate was under 50 per cent and when you do that you struggle to put anything on with any purpose.
“Every time we tried to put something on, someone dropped the ball, made an error or gave away a penalty.
“It’s the worst performance since I’ve been at Fev and one of the worst I’ve seen in a long time.”