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Lukaku scored 23 goals in 36 top-flight outings in his debut campaign for the Nerazzurri following an €80 million (£80m/$94m) switch from Manchester United and hopes the best is yet to come.
"Thank you for supporting the team throughout this season. To all of my team-mates, you guys have been wonderful. I would give my all for you guys every single day."
It is the first time they have earned in excess of 79 points without winning the Scudetto.
However, despite that strong finish, Conte appeared unhappy with the board and publicly criticised them after Saturday's game.
Conte accused the Inter hierarchy of showing alack of supportwhen the side was struggling for results earlier in the campaign and that they failed to protect him and his players from criticism.
He also expressed his "great pride" at the club's achievement in matching the points tally from their treble-winning year, and said"credit must be given to everyone," including Conte and his coaching staff for their hard work.
With their domestic season now over, Inter can turn their attentions to the Europa League.