The victory was Canada's first-ever World Cup finals win and sent them to the top of Group B, but the celebrations were overshadowed by Kone's injury in the 55th minute after a challenge from Qatar midfielder Assim Madibo.
Kone was treated on the pitch for several minutes before being taken away on a stretcher, requiring oxygen and pain relief. Marsch, who was close to the incident, said the moment affected everyone inside the stadium.
"It happened right in front of the bench; we could all hear it," Marsch said. "Your heart goes out to him. Everyone is a little shaken because of the nature of the injury and because Ismael is such a big part of the heart of our team."
The Canada boss confirmed Kone was in hospital preparing for surgery and praised the midfielder's character after the injury.
"He was waving to the crowd and making everyone else feel at ease with the fact that he's injured. It's an incredible statement about Ismael as a person," Marsch added.
"Everybody was crushed when it happened, but we had to find a way to stay focused."
Madibo was shown a red card for the challenge and later visited the Canada dressing room to apologise to Kone. Marsch said he did not believe the Qatar player intended to cause serious harm.
"The player apologised to Ismael. He came into the dressing room and apologised to him, and Ismael told the team," Marsch explained. "I don't think he meant such a gruesome tackle or such a situation."
Despite the difficult moment, Canada produced a memorable performance. A Jonathan David hat-trick inspired the hosts to a dominant victory, with Cyle Larin, Nathan Saliba and an own goal from Qatar completing the rout.
Canada controlled the match from the start, with David playing a key role in their attacking display. Larin opened the scoring after 15 minutes before David struck twice before half-time to put Canada firmly in control.
Qatar's problems increased after Homam Al Amin was sent off for denying a clear goalscoring opportunity, while Madibo's dismissal after the Kone incident left them with nine players.
Saliba, who replaced Kone, marked his introduction with a superb free kick to make it 4-0 before Canada added two more goals to complete their biggest World Cup victory.
Marsch described the result as a special moment for Canadian football.
"No Canadian will forget this day," he said. "There will be 40 million people who will say they were here."
Canada now lead Group B on goal difference ahead of Switzerland, who they face on 24 June. A draw would guarantee top spot and allow them to play their next knockout match in Vancouver.
For Marsch, the challenge is now to build on a historic night while supporting Kone during his recovery.
"We are very proud of what we are and who we are," he said. "This will drive us to do everything we can to win the group and make a run at this tournament."
