Ten Hag warns FFP regulations will stop Man Utd signing new striker
Martial has been ruled out until April after undergoing surgery on a groin injury but United, in common with several leading English clubs, have appeared more interested in reducing rather than bolstering their squad as they come to terms with the impact of the Premier League's profit and sustainability rules.
"I looked but there is no space," said United manager Ten Hag. "No space on FFP to do something about this lack of quantity in the striker position.
"Of course, we have (Marcus) Rashford who can play as a striker, I think also we have some other alternatives, creative.
"It's clear now Anthony is out for a couple of months. It's a gap in our squad. Clear."
Ten Hag was speaking to the media for the first time since United poached Omar Berrada from local rivals Manchester City as their new chief executive.
Berrada's arrival at Old Trafford is one of the first major appointments made by United since British billionaire Jim Ratcliffe took a 25 percent stake in the club for $1.3 billion (£1.02bn).
United have been without a permanent chief executive since Richard Arnold left at the end of last year.
"It gives spirit in this whole club," said Ten Hag of Berrada's move.
"Everyone notices that this club is going into a period of changes but it's because we want to achieve high targets, so standards have to change."
The Dutchman added: "We understand we have to change, and we started that process last season with the dressing room.
"But also many departments so I am very happy that I get support."
United's short-term focus is on their FA Cup tie away to fourth-tier Newport on Sunday, with the knockout trophy representing their last remaining realistic hope of silverware this season.
The match is set to mark the long-awaited United debut of pre-season signing Altay Bayindir.
"Yeah, he will be in the goal," Ten Hag said of the former Fenerbahce goalkeeper.
"He played in a big club in Turkey under big pressure, so he knows how to deal with it.
"We were all very convinced when we brought him into this club...We're looking forward to Sunday. Altay, very motivated of course and he can't wait for this moment."