Archer was speaking about defeat in their Carabao Cup quarterfinal against Liverpool.
He told the Daily Echo: : "It's obviously disappointing but it's football. Things happen in football.
"It's part of the game and you have to move on from it. It's always disappointing when someone loses their job. He was close to us but it's a part of the game, we have to move on."
On Martin's replacement, Archer also said: "You don't have a clue until they walk into the building. No clue on that one."
On caretaker coach Simon Rusk's influence on the night, the striker, who scored on the night, also said: "We didn't really have a way of playing.
"I would say it felt quite freeing.
"We made the most of it. We used our abilities and what we were capable of as players. Our individuality.
"Adam Lallana and the skipper (Jack Stephens) spoke with the gaffer. They spoke about togetherness. It's down to us and what we do on the pitch.
"In the second-half, we got a bit closer to them. We applied more pressure going forward. We had a right good go at them. We dug deep and we stuck to the gameplan quite well."
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