Slovakia captain Hamsik scored a screaming effort - having set up the first - as Slovakia beat Group B rivals Russia 2-1 in Lille to secure their maiden European Championship win.
Hamsik's performance prompted Slovakia coach Jan Kozak to claim: "Napoli has become too small – he deserves a bigger club for his performances."
However, the 28-year-old is keen to see through a 10th season at the San Paolo, having helped Napoli back into the Champions League under Maurizio Sarri in 2015-16.
"I still have two years of contract with Napoli and my future is here," Hamsik told Gazzetta dello Sport.
"There's the Champions League to play and we want do great things. The club is improving the right way, aims for bigger and bigger goals.
"As you know, it doesn't depend only on me, anyway I didn't think to leave. And I guess also the club didn't think that."
Hamsik and Slovakia face England in their final group game, knowing victory will secure a place in the last 16.
He continued: "Getting through to the next round is our goal, but the third match against England will be a play-off.
"I enjoy this moment and the team made the finals of the European Championship. This is a great satisfaction.
"We had never won before in a UEFA tournament. This is a special time."