Handzus has zero points and a minus-five rating over the Blackhawks' last eight games. He was taken off the second line recently and played the last two games centering the third line.
"I haven't played great," Handzus said after the Blackhawks' morning skate on Tuesday. "I've got to be better. I've just got to be better.
"I haven't skated really well. I haven't been hard on the pucks, too. I just need to work on it. Everything picks up after that. I thought last game was a little bit better. I just need to keep building and get better and get where I need to be."
Handzus said he understands the decision to remove him from the second line. He skated with Bryan Bickell and Kris Versteeg on the third line again during the morning skate on Tuesday.
"You're always disappointed when something doesn't work and should be working," Handzus said. "I was disappointed, but I understand it because I didn't play very well. I just have to worry about how I play and how I need to play and how I can help the team.
"[Line changes,] that's usually what happens when as a whole we didn't play as well the last 5-6 games. The changes kind of sparked us the last two games. I thought the last two periods we played better. Hopefully we're on our way up and I'm on my way up, too."
Quenneville also believes Handzus' play had improved in the Blackhawks' last game, a 5-3 win over the Edmonton Oilers on Sunday. Quenneville said Handzus needed to especially keep up his pace to be effective.
"I thought he was much better last game whether it was off the stretch, off the break and coming back," Quenneville said. "I thought he had some good games. When his pace is a little bit off, it's noticeable. When he's on his game, he brings a lot to the table in playing the right way and some defensive responsibility for our team."
Neither Handzus, who was recently selected to play for Slovakia in the Olympics, does not believe he would benefit from sitting out the Olympics.
"I mean it can go both ways," Handzus said. "I remember the last Olympics I played and I was OK. I remember guys who take the two weeks off, and they couldn't get going for a month or a so. I think the travel is a little bit different. It's most concerning for everybody. I don't want worry about it that much."
Quenneville said he will be watching Handzus' minutes going into and coming out of the Olympics.
"I think with his situation he's excited about it," Quenneville said. "At his age and a chance to represent his country and a chance to be on a team that can surprise some people as well. We'll keep an eye on him as far as where he is at with rest and how his energy as we come out of it. Actually, something we're monitoring actually as we're going along here now. Take a closer look out of it. I think it'll be fun for him. He's excited to be playing with [Marian Hossa].