Rodrigo's second-half strike rescued a point for Leeds after Lucas Paqueta's penalty and Gianluca Scamacca's effort had cancelled out Wilfried Gnonto's opener.
Leeds remained 14th in the table, two points above the relegation zone, while West Ham edged out of the bottom three after this draw followed five straight league defeats and extended their winless run to six matches.
Marsch said: "I'm pleased with the way we pushed the game at 2-1 (down), but I'm very frustrated that it took our players to go down a goal in that point of the match to play to their potential, their ability and fearlessness.
"The first half for me wasn't good enough. We played backwards too much, we invited the opponent into the match too much.
"There's a little bit of frustration and confusion about how to get them to be what I know they can become, be the team I know we can be.
"And how to have them remove this idea of pressure and stress and focus on exactly what the game needs to be and then perform at our level."
Leeds, who have taken two points from their three league games since resuming after the World Cup break, were denied victory by two superb saves from Lukasz Fabianski, who kept out two more Rodrigo efforts.
After the match, Marsch and his players donned farewell T-shirts in tribute to Mateusz Klich, who stepped off the bench just after the hour to make his final appearance for the club.
Leeds later confirmed the Polish midfielder, who played a key role in the club's promotion under Marcelo Bielsa in 2020, has received an offer from a Major League Soccer side, reported to be Wayne Rooney's DC United.
Klich's contract at Leeds does not expire until 2024, but Marsch was unable to guarantee the player sufficient game time, while his new contract offer is too good for him to turn down.
"This was not a black-and-white decision," Marsch added. "This was a lot of different discussions, Klichy being provided with an opportunity that he thought was a little bit more long-standing and provided stability for his family and try something new.
"It won't be easy to lose him and if we were to say that between he and I, we are not absolutely sure it's the right decision, but I certainly wish the best for him."
West Ham boss David Moyes said he was satisfied with his side's performance after they secured their first league point since October.
Moyes said: "We fought hard. It was a good old-fashioned game at times. I felt when we went 2-1 up we'd go on and win the game and if anything we gave the game back to Leeds.
"But it's a step in the right direction. Getting a point away at Leeds United is a good result for lots of teams. It is for us at the moment."