Fernando Santos' men dropped their first points in Group G with a goalless draw at home to Bosnia-Herzegovina last Friday, and find themselves in a three-way tie for top spot.
Slovakia's 2-1 victory over Latvia moved them alongside the Greeks, but Karagounis sees no reason why they cannot give themselves some breathing space over their opponents tomorrow night.
"We wanted to win (in Bosnia), but even with the draw we remain at the top with the other two strongest teams in the group," the Fulham player told Era Sport.
"The match with Slovakia will be difficult but we will play to win. Our goal in every match is to win.
"We have confidence and know we can beat any opponent."
Slovakia's win over Latvia saw both midfielder Vladimir Weiss and defender Martin Skrtel leave the pitch with knee and head injuries, respectively.
However, the pair have returned to training and coach Michal Hipp is hopeful they will be able to play some part tomorrow.
Bosnia-Herzegovina also sit alongside Slovakia and Greece on seven points but have the edge over their rivals on goal difference, and continue their qualifying campaign at home to Lithuania.
Victory tomorrow would see Lithuania, who beat Liechtenstein 2-0 last week, move level with their opponents in a close-knit group.
However, Bosnia midfielder Sejad Salihovic is determined not to let that happen.
He told www.nsfbih.ba: "We managed to do well in Greece.
"I think we also have a great chance at home of beating Lithuania, but we have to be careful. It will be a tough game we have to prepare for."
Latvia and Liechtenstein are both without a win in three attempts so far, but something will give when they meet in Riga tomorrow night.
The Latvians will have the advantage as hosts, but coach Aleksandrs Starkovs told www.lff.la: "While Liechtenstein are worse than us on paper, they are a hard nut to crack.
"They are an uncompromising, disciplined team. We are preparing very seriously for this match."