Marsch upset with Argentina's half-time delaying tactics
The game was goalless at the interval and after the half-time break the Canadian players were left standing on the field for several minutes waiting for Argentina to emerge.
The world champions scored within four minutes of the re-start and went on to win 2-0 with American Marsch suggesting they were using the time for some extra video analysis.
"When they were waiting, I knew that they were looking at video and they were analyzing how they wanted to play against us," he told the post-match press conference.
"Now, I wish again, the referees would manage that. If we were five minutes late, we'd get a fine. There'd be a big problem. Let's see what happens with Argentina," the former Leeds United manager said.
Marsch said he had told his players to expect a change in approach from Argentina after the break.
"In the end, I just made sure that the players knew that they were going to come out with a new plan and they basically rotated a little bit more to three, but we still dealt with it," he said.
"Argentina should be fined. OK? Fined. Write that. Olé. La Nacion," he said, directing his comments at the Argentine press.
Marsch was more positive about his own team's performance after the 48th ranked team in the world, who he took the reins of last month, caused the world number one plenty of headaches.
"Big picture is we, I thought, had a good performance and especially when we were able to execute our tactical plan, we made it very difficult on Argentina and really could have had some goals, could have had the lead," he said.
The game was just the third with Canada for Marsch who led the team in a 4-0 friendly defeat away to the Netherlands before a 0-0 draw in France against Didier Deschamps's team.
"I said to the team afterwards that we take this game, but we also take the three matches," he said.
"It's been unfair to them in some ways to be put in a situation to expect to have early success with a new manager in a new situation when we have to play these levels of opponents," he added.
"But I think we've learned a lot from it and mostly we've learned that we can play. We can play with these teams," added Marsch.
Canada face Peru and Chile in their other Group A games as they look to make it into the quarter-finals .
"I think where we sit right now, as painful as it is to know that we let this game slip away from us when we had certain things in control, I do believe that we come away from the three matches stronger, clearer and more prepared, hopefully more mature for what it's going to require," said Marsch.
"But Peru will be another really tough match and we can't assume anything and we have to keep pushing this group to develop, to improve, to get better," he added.