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.
Stoke have won 2-0 in both of their two home games against Swansea in the Premier League and Mark Hughes will hope that history repeats itself on Wednesday.
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.
Monk is concentrating on the threat Swansea are capable of posing and has urged his side to build on their derby triumph.
"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 are a point and three places worse off than their opponents and one of the reasons for that is a lack of clean sheets.
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.
Hughes has injury concerns over Robert Huth (knee) and Marko Arnautovic (ankle), so Geoff Cameron is likely to start at centre-half with Marc Muniesa taking over at full-back.
On-loan striker John Guidetti has yet to start since his move from Manchester City and after Peter Crouch and Peter Odemwingie both scored in the 2-2 draw with Southampton, the Swede may have to bide his time.
