Maddison, who missed the final through injury, spoke after the final whistle and took aim at Terry, who was suspended for Chelsea's Champions League final in the 2011/12 season against Bayern Munich but came on at full-time in a full kit.
"I did not want to do a John Terry," he said.
"I know I played a big part in the lead up and I deserved this just as much as all of us."
On Instagram, Maddison posted an image on his story of him in smart attire, again taking a dig at Terry.
"From suit," followed by a picture of him and Johnson with the Europa League trophy in his kit. He added: "To kit. Full @johnterry.26 mode. Anything to say tonight John? laughing face emoji white love heart."
The legendary defender joked about Spurs' woeful Premier League campaign and joked about how Spurs have found little success in the trophy department in recent years.
"I remember my first trophy ah bless them. Get the tequila out. Great season from you boys, you should be all proud! 16 to go...
"After that performance, I think you have a chance. You just have to live for 900 years."
Terry followed that up with another Instagram story of him showing fans his trophy room that includes a number of Premier League titles, domestic cups and a Champions League trophy.
"Good morning everyone. Have a lovely day *blue love heart* *trophy emoji* *eyes emoji*."