O’Shea was repeatedly pressed on the issue throughout the media conference alongside goalkeeper Caoimhin Kelleher.
He added: “It’s not a leading role, I’m the assistant. The leader is the boss and that is clear.
“I don’t know why there has to be this constant. The boss is the boss, it’s very simple. The players know that, you can ask Caoimhin about that. The meetings that were coming across, the plans in place.
“So I don’t know why you have to keep going on about that. For me personally, it’s clear from the staff’s point of view and the players’ point of view.”
Goals from Declan Rice and Jack Grealish, two players who had previously represented the Republic of Ireland at either senior or under-21s level, were enough to give England victory on Saturday.
While the hosts were second best throughout the contest, O’Shea welcomed the fact that the side are back at the Aviva Stadium just three days later to face Greece.
“You play against a team that has just been in the Euros final and you know you’re going to be under plenty of pressure in a game like that. The fact that it was England brings that extra bit of scrutiny too.
“Clearly room for improvement, we know that. We know England were the best team on the day, but thankfully we have another chance to put in a performance against Greece quite quickly.”