The 19-year-old completed his move to Old Trafford on Tuesday, with reports suggesting that United could pay as much as €80 million (£58.6m) for his signature - the highest transfer fee ever paid for a teenager.
Martial scored just 11 goals in 52 Ligue 1 matches for Lyon and Monaco and Carragher believes the fee is a huge price to pay for an unproven prospect.
"I think so," Carragher said, when asked if he was surprised by the price.
"He's the most expensive teenager in world football, so it's a big price. He comes with a lot of potential, which is expected at that age, just getting to the French squad as well.
"With Monaco going out of the Champions League [in the play-offs] as well, it made it easier for Manchester United to get him.
"But it's certainly a position they needed to strengthen, striker-wise, with the players that have moved on.
"He's a young player and when you talk about potential you're still not quite sure but for that price, he must be some player."
Several Premier League managers have suggested that the transfer window should shut earlier as not to affect on-field matters, and Carragher is looking forward to the focus turning back to the football.
"There's a lot of excitement, last-minute deals getting done," Carragher added.
"You always wonder why it takes so long to get the deals done. You look at the Manchester United-Real Madrid one [with David de Gea] as a case in point really, why you have all summer and it goes to the wire and it doesn't quite get done.
"It's exciting for the fans. I don't think managers like it. I think they want to call it to a halt once the football starts, but I think for the man on the street it's quite exciting.
"It's done now; get on with the real stuff - the football."