But after selling Javier Hernandez, Robin van Persie, and not signing Radamel Falcao after his loan deal, and then sending Adnan Januzaj to Borussia Dortmund, Van Gaal moved for Martial.
"It was a signing out of the blue really," Carragher told Sky Sports.
"United missed out on Pedro and Martial is not a household name in this country; he was an up-and-coming player in France.
GETTY
Anthony Martial joined United on deadline day for an initial £36million
"The price that was paid obviously raised eyebrows but, like with any transfer fee, if any player succeeds and does well he is worth it."
United are down to just Martial and Wayne Rooney up front, with James Wilson set to join a Championship club on loan.
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Van Gaal's side have scored just three goals in four games - one of which was Kyle Walker's own goal on the opening day of the season - and former Liverpool defender Carragher reckons bringing in Martial is a huge risk.
"Eyebrows were raised when Raheem Sterling left Liverpool for £49m, but he has started the season well, City look fantastic and, at this moment, it looks like a good buy," Carragher added.
"The add-ons could take the Martial deal to £50m-£60m, which is a lot of money for a young player.
"For the price to be that high, it shows that there must be something there, that Manchester United, Louis van Gaal and Ed Woodward think it is worth paying. It is certainly a gamble, but he must have great potential."
Watch Man United target Anthony Martial miss an open goal - and celebrate like he's scored