At 0-0, Archer's spotkick was saved before United fired three goals past Aaron Ramsdale to win 3-0.
Penalty taker Adam Armstrong was left on the bench, while Ben Brereton Diaz - who has scored seven career spot-kicks - was passed over for Archer.
Martin told the Daily Echo: "Well, Ben's quite a bit older than Cam (regarding his record). We've had a chat about it.
"Cam has practiced a lot over the last two weeks during the intentional break whilst he's been here and Ben hasn't. He's done brilliantly with them.
"At some point, he's a number nine and he's going to want to take penalties - and he felt really confident to take one and Ben was happy for that as well.
"It is one of those things, if he scores, he's off and away. But he didn't, so of course, it's going to get questioned."
Martin added: "It's on me and the decision we made and he's missed it. It's just the wrong one."