Suter and Parise signed with the Minnesota Wild on Wednesday morning, turning down offers from multiple teams, including the Hawks.
"I talked to the agents numerous times," Bowman said on a Wednesday evening conference call. "We made a very appealing offer to them. They didn't grow up in Chicago. Zach is from Minnesota, and that's something we can't change. We have to respect that and not dwell on it."
Bowman reiterated several times the players' desires to play near their homes. Suter is from Madison, Wis.
"You can't dwell on it too long," Bowman said. "I think we made an impressive case. That's the feedback we got from the agents. The family thing is what carried the day."
Bowman expressed satisfaction with the players the Hawks currently have in place, but said the organization would not hesitate to try to improve the team via free agency or in a trade. The Hawks have a full roster, but still are about $8 million under the salary cap.
"Our objective isn't to make a splash, it's to win hockey games," he said. "It's not like we have seven holes to fill. Last year's team had 101 points, and I think there was a lot more to give even if we brought back the exact same roster. There were ways to be better with that group."
Brodeur was a free agent for a day before re-signing with the New Jersey Devils on Tuesday morning.
"Marty is the winningest goalie in the history of the game, so in some ways it would be foolish not to discuss that with him," Bowman said.
"We're very comfortable with our goaltending," Bowman said. "We wouldn't be doing our job if we didn't talk to them (Parise, Suter, Brodeur)."
The Hawks have made one free-agent signing, inking defenseman Sheldon Brookbank to a two-year deal on Sunday.
"That was one of the pieces we were looking to upgrade from last year," Bowman said. "Another right-hand shot, a defenseman with a little bit stronger defensive profile. Penalty killer, steady player, has a little physical element to his game. That's something we want to add into our mix a little more.
"We're going to keep pursuing different things. Its only July 4. The summer hasn't played itself out yet."