The Italians had led early through Romelu Lukaku's penalty but the Spanish side responded through two Luuk de Jong headers, only for Diego Godin to equalise for the San Siro side.
Diego Carlos, who was perhaps lucky not to be sent off for giving away the spot kick, forced a winner late on with an overhead kick which took a hefty deflection.
Conte was also involved in an argument with Sevilla midfielder Ever Banega, reportedly over his hair transplant, but insists that he has no ill feelings at how the game panned out.
"We worked hard, it was a very tough season in many ways, so it’s only right to take a little rest, face the situations and make the decision that is best for Inter," he told Sky Sport Italia.
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"There is absolutely no bitterness. There might be different views on things, but we’ll evaluate everything.
“It has been difficult and we’ll figure things out. It has been wonderful for me to be the coach of Inter, I thank the owners who allowed me to go through this great experience.
“These lads worked hard, grew so much and have improved. They reached the Europa League Final, many were at their first experience in Europe, so between the Champions League and Europa League, at least many of our young players gained experience for the future. That is important going forward, also for self-confidence.”
Conte has been linked with an exit from Inter and promised to clarify his future properly in due course.
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“You don’t know what my opinion is. I’ll have my say with a cool head when the time is right. The important thing is that whatever we do is done in harmony.
“Regardless of everything, it was a positive experience and I thank those who gave me this opportunity. I was welcomed beyond the rosiest expectations. I gave a great deal to them and the players gave their all to me.
“There is no rancour, from me or the club. There are people I already worked with, so that’s not the issue.
“If you think I will step back, I won’t. I said what I think, you heard my words and they have not changed.”