The Argentine struck twice to seal an incredible comeback win for the Nerazzurri, and is hopeful that his side can use the result as a springboard for the rest of the season
Andrea Stramaccioni's side found themselves 2-0 down after just 20 minutes at Stadio Angelo Massimino, but two goals from Palacio - including an injury-time winner - followed Ricky Alvarez's strike in the second half and sealed a remarkable win for the visitors.
Palacio believes his side deserved the victory following their performance, and is hopeful that they can now go on a run of form after an inconsistent spell.
"It was a really important win, it was a tricky match but we did it," the 31-year-old was quoted as saying by the club's official website. "Once again we played badly in the first half and well in the second. What's important is that the team played well. Now we'll try to continue in this vein."
Antonio Cassano was dropped for the encounter on Sunday afternoon after a training ground altercation with Stramaccioni, leaving much of the attacking burden on Palacios' shoulders, as Inter struggled to cope with their depleted attack.
However, the Argentine insisted he felt no additional pressure before the game, stating: "I'll continue as I always do."
The result means Inter move into fourth spot at the expense of Lazio, with both sides on 47 points after 27 games.