After finishing second in Serie A, Inter fell short in the Europa League, suffering a dramatic 3-2 loss to Sevilla in the final on Saturday (AEST).
The longest Europa League season came down to a defender's spectacular shot and a striker trying to keep it out.
Luuk De Jong struck twice for the Spaniards in the first half before Diego Carlos, who conceded a penalty early on, tapped in the game-winning goal.
Inter started an onslaught on Sevilla's goal in the dying minutes of the game but for all that Sevilla's well-positioned defense stood firm and protected the narrow lead to the final whistle, clinching a record sixth Europa League title.
Sevilla's lead was short-lived as well as Diego Godin headed in a deep free kick from Marcelo Brozovic to level the score.
Lukaku failed to beat Yassine Bounou when one-one-one and Sevilla took full advantage.
The title is the first in the coaching career of Julen Lopetegui, who is in his first season with the Seville-based club.
Victory over Inter continued an incredible record of La Liga clubs against non-Spanish opponents in UEFA finals, with 15 consecutive wins stretching back to 2001. He had lost his job as Spain coach on the eve of the World Cup over his decision to take over Real.
The lone survivor from that side, Jesus Navas, proudly lifted the trophy as captain in Cologne on Friday night.
"It is only right that we analyse the entire season, look at everything in a very calm way and try to plan the future of Inter, whether it's with or without me", said Conte.
Defeating Inter made it six titles from six finals for Sevilla, which has won every time it's reached the last eight.
Sevilla's celebrations post-match saw the players wear shirts honouring the passing of former players Reyes and Puerta.