The new head coach faced a baptism of fire against in Saturday's crunch clash with Cardiff City, but masterminded a 3-0 win in his first game in charge since replacing Michael Laudrup.
Monk faces a tricky trip to Stoke on Wednesday for his first away game at the helm and the Britannia Stadium has not been a happy hunting ground for Swansea.
Hughes' side beat Manchester United 2-1 in their last home game in the top flight and followed that up with a 2-2 draw at Southampton on Saturday.
"It was a tough week but I just want to carry on pushing the principles that we stand for and not let the players relax," the 34-year-old said on Monday.
"The players are willing to put the hard work in and take that out onto the pitch."
Swansea's league form has been far from impressive in 2014 and the victory over Cardiff was only their second of the calendar year.
Monk's side are 10th in the table, but are only seven points better off than basement side Fulham.
Stoke's defence was difficult to breach under Tony Pulis but there have been only six games this season in which teams have failed to score against them in the top flight.
Midfielder Jonjo Shelvey could be involved for the visitors after recovering from a hamstring problem, but striker Michu is unlikely to feature as he continues his recovery from a knee injury.
