The decision taken by the Tokyo manufacturer comes as Espargaro’s future with the team has been in doubt.
The new parts taken to Mugello last week were a swingarm and a chassis, with one of each fitted to Marquez's RC213V.
After it was announced that the six-time world champion was to undergo surgery and be sidelined indefinitely, Honda decided that those parts would be passed on to Japanese satellite team rider Takaaki Nakagami, rather than Marquez’s team-mate.
Espargaro said on Thursday: "In the last race Marc was testing a new chassis and swingarm, especially this last part has some improvement, more than the chassis, and Honda's decision is to pass the parts to Taka, who is also a factory rider.
"I'm going to keep fighting with the tools I have, just as I have done since the beginning of the season and that's it, that's all.”
Espargaro said he accepted Honda's decision to hand over the part to a rider from the satellite LCR team, and said “you will have to ask the question to the person in charge, it's not my job.”
"It's not for me to ask myself these questions, Honda have made a decision and I abide by it,” he said at Montmelo on Thursday.
“I am a rider and I have to ride the bike as fast as I can and that is what I try to do every weekend. The decisions of who gets the material or who evolves the bike is entirely up to Honda and you will have to ask the question to the person in charge, it's not my job.”
But he added: “Of course I want the latest on my bike and as much new stuff as possible to improve the situation, especially when the situation is not going well.
“What you want is to have a lot of new parts to turn it around, this is not happening and we only have a new chassis and swingarm and Taka is going to use them.
“It is what it is, I'm not saying it in an angry tone or anything, it's a Honda decision, I accept it and I'll ride as fast as I can with the bike I have in the box.”
Despite the move, Espargaro said he “still feels loved by Honda” and remains “fully committed to the brand until the end of the year, and maybe with a renewal.”
He added: “But so far this is the situation and I accept it perfectly. Taka is a fast rider, also very valid to try this kind of things and he is much more tied to the factory than me, I understand that he has the opportunity to try new parts and I respect that.”
