Morocco, 2022 World Cup semi-finalists and Africa Cup of Nations champions, proved decisive in front of goal, with Azzedine Ounahi striking twice either side of a Soufiane Rahimi stoppage-time finish to secure a quarter-final place.
Despite the scoreline, Marsch was adamant his side had been the better team for long stretches.
"We totally controlled the match," he said. "We were the ones more likely to win the game, but goals change games so they could sit back. But overall in the match we were better than them."
He added: "We had 11 incredible performances in the first half. We were unlucky not to get the lead. We should've been on top of the game."
Canada registered more attacking intent in phases and created chances throughout, but Morocco's clinical edge proved decisive, punishing a set-piece situation for the opener before capitalising on a defensive error for the second.
Marsch pointed to those moments as turning points, while maintaining that the overall performance reflected Canada's growing identity on the global stage.
"I challenged the players to understand that we can play like this all the time," he said. "Against the best teams in the world we can be better on the day. Can we build a real Canadian DNA?"
However, Morocco head coach Mohamed Ouahbi strongly rejected the suggestion that Canada had been superior.
"It takes some nerve to say that when you lose 3-0," he said, though he did acknowledge the intensity of Canada's pressing game and noted adjustments his team made to bypass it by playing longer passes into space.
Canada's task was made harder by the absence of key defender Alphonso Davies, who missed the match after a hamstring issue. Although a scan showed no significant injury, the Bayern Munich full-back was not risked and was ultimately deemed unavailable despite attempting to test his fitness at half-time.
The defeat also marked Canada's exit as the first of the three co-host nations, but Marsch urged perspective after a tournament that delivered historic progress.
Before this World Cup, Canada had never progressed beyond the group stage. This time they recorded two wins, including a 6-0 victory over Qatar - the largest margin of victory ever achieved by a CONCACAF side at a World Cup - and advanced to the knockout rounds as runners-up in Group B.
Players such as Jonathan David, Stephen Eustaquio and Alphonso Davies were central to a campaign that defied pre-tournament expectations, with Canada showcasing a high-intensity style that earned praise even in defeat.
Morocco, meanwhile, move on to the quarter-finals for the second consecutive World Cup and will face the winner of France and Paraguay on July 9 at Gillette Stadium.
Marsch, however, remained defiant in his belief in the project, even going as far as to compare his side favourably to their opponents.
"I'd rather be us than them," he said. "As good as Morocco is, I'd rather be us. I'm really proud of our guys. We went after the game."