Napoli's hopes of making the knockout phase for the first time since elimination by eventual winners Chelsea in 2012 were left hanging in the balance by a scoreless draw at home to Dinamo Kiev on Wednesday.
Although still top of Group B, defeat for Maurizio Sarri's men in their final group game, away to Benfica in a fortnight, would bring a spectacular end to a campaign that started with so much promise.
Hamsik was one of several players who saw shots on goal thwarted by Dinamo 'keeper Artur Rudko at the San Paolo on Wednesday.
And the Slovakia midfielder, who was on target last September when Napoli beat the Portuguese giants 4-2 at home, has called for a more clinical performance when they travel to Lisbon on December 6.
"We know a point will be enough to see us through, but we won't be playing for a draw," Hamsik said.
"More than anything, we have to play better than we did tonight. It's a shame, because a win would have made things a lot easier.
"But we're up near the top of the group and we'll go to Lisbon looking to qualify."
Napoli had been given a pre-match incentive when direct qualification rivals Benfica stormed to a 3-0 lead over Besiktas in Istanbul.
By the time the Italians had finished their warm-up and returned to the pitch for kick-off, Besiktas had drawn level 3-3 to secure a share of the spoils.
It gave the Turks a precious point, left them only one point adrift of Benfica and heaped the pressure on Napoli's players ahead of facing a team they had beaten 2-1 in Kiev at the start of the competition.
Sarri admitted the 3-3 result had a direct influence on his players: "We went off after the warm-up and Benfica were leading 3-1, then we came back and it was 3-3.
"This was a mental blow for the players because it meant we could no longer qualify directly. It's terrible, we shouldn't be allowing ourselves to be influenced like that."
Napoli are still missing prolific Polish striker Arkaduisz Milik, who scored twice in their opening win over Dinamo and once in the 4-2 win over Benfica, as he continues his recovery from a knee ligament injury.
His absence was felt acutely on Wednesday as Dries Mertens, Lorenzo Insigne and Hamsik missed a series of chances to secure a third win in the group and virtually wrap up qualification.
Anything less than a draw away to Benfica would end Napoli's interest in the competition, a fact that didn't escape the fans who booed and whistled Napoli off the pitch at full-time.
Sarri said later: "I don't think our performance deserved to be whistled. The important thing is we remain united, because things could get much better in the near future."
Milik, bought from Ajax in the summer as a replacement for Juventus-bound Gonzalo Higuain, is expected to return to the fray some time in January.
The Champions League last 16 begins in February.