The Wild (37-36-9), who failed to qualify for the playoffs for the first time in seven seasons, signed Zuccarello (five years) and Hartman (two years) on July 1.
"Last season was disappointing," Zucker said Wednesday at Da Beauty League, a weekly set of 3-on-3 games that feature NHL players with ties to Minnesota. "It's not where we wanted to be, and we have to fix that this summer. We made a couple of moves that should be good for us. … We have to get after it hard this summer and get to training camp."
RELATED: [Zuccarello agrees to five-year contract with Wild | Hartman agrees to two-year contract with Wild]
Zucker has been mentioned in trade rumors during the past few months, but he remains with the Wild. The 27-year-old forward had 42 points (21 goals, 21 assists) last season after setting NHL career highs in goals (33), assists (31) and points (64) in 2017-18.
"It's not easy," he said of the rumors. "But you have to set it aside at some point and be ready to go."
Parise, who led the Wild with 28 goals and 61 points, said he is pleased with the signings of Zuccarello and Hartman after Minnesota finished 27th in the NHL with 210 goals scored. The Wild scored one goal or fewer in 24 games.
But Parise, a left wing who turns 35 on July 28, said Minnesota was missing a playmaker, a role Zuccarello is expected to fill. The 31-year-old has 355 points (114 goals, 241 assists) in 511 NHL games with the New York Rangers and Dallas Stars.