The premier insisted that his government have worked hard to kick violence out of football, but noted that other problems are difficult to deal with
The first day of Euro 2012 was overshadowed by an assault from Russian fans on Polish stewards inside Wroclaw's Municipal Stadium following the team's victory against Czech Republic on Friday.
As Poland head into their second match in the tournament, against Russia, there are fears that violent clashes between fans of the two teams will take place inside and outside the National Stadium in Warsaw.
Mr. Tusk has been criticised for taking little action against the matter, but he has conceded that hooliganism, and other issues, are difficult to eradicate from football.
"For one, no one can accuse me of not doing anything against hooliganism in Polish football," he told reporters.
"Strong actions have been made by our government, but I am aware of the fact that there is still a long way to go to kick racism and anti-semitism out of Polish stadiums.
"I can assure you that we will take care of it strongly after the tournament.
"We cannot treat these rare incidents as a sign of rising tensions. People that were identified by our police at the stadium in Wroclaw will face action, like everyone else causing problems.
"We are preparing ourselves but also doing everything not to raise the temperature ahead of [Tuesday's] match.
"Polish police are prepared very well for the tournament and despite the festive atmosphere they are ready to step up whenever required. I believe that the toughest games, like the one from today [Poland versus Russia], are still to come."
However, Mr. Tusk said that he does not think that these incidents will ruin the tournament, and has called on his countrymen to continue the good work they have displayed in welcoming visitors from across Europe.
"I appeal to everyone to show once again what warm hosts we are, and not to get ourselves involved in any disturbances," he added.
"I think that up to this moment we have shown that we are good hosts, welcoming those who have come for Euro 2012.
"Tonight, 40,000,000 fans will unite and focus on the game in Warsaw, but only for football reasons and hopefully we will make history."