The striker's effort came five minutes before full time to condemn AC Milan to a 1-0 defeat.
"It's an important goal for Inter and the most important goal of my entire career," Palacio told Sky Sport Italia.
"We deserved this victory and it will give us more confidence, as derbies are always important. Now we can go on the Christmas break happy and then return to do even better."
Inter coach Walter Mazzarri commented: "The goal seemed cursed again today, as we kept going close and missing the finish or the final pass, but we got there in the end.
"Unfortunately we have thrown away too many victories and therefore have four or five points less than we deserve, but looking at how we began and the project then we can't help but be satisfied."
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