The Swans finished ninth in the Premier League and also won their first major trophy as they lifted the Capital One Cup thanks to a 5-0 final victory over Bradford City at Wembley.
Monk is proud of what has been achieved by the club, especially as they only came up from the Championship a couple of years ago.
"A top-ten finish and a first major trophy have made it the most successful season in the history of Swansea City," captain Monk told the club's official website.
"The clubs that finished above us are the teams that our fans used to watch regularly on Match of the Day.
"Now it is us that are competing with them on a weekly basis. With the way it's played and the quality of players and teams, it is the best league in the world.
"To go to Wembley and lift the League Cup was an amazing feeling too. It was a huge honour and privilege to do that.
"As a club we have a lot to be proud of - that's the players, the staff and the fans. "
Swansea face an even tougher challenge next season with the added workload of European competition, but Monk hopes they can go from strength to strength.
He said: "You do have to pinch yourself sometimes when you look back at how well we have done because it is a massive achievement, but the important thing is to keep pushing ourselves on.
"We have to continue improving. We have Europe on the agenda now, so we all have to work harder next season to ensure we maintain our progress."