Argentina international Higuain is to undergo back surgery and may be sidelined for around two months, leaving France international Karim Benzema as the only recognised striker in the squad.
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"After all the signings they have made, at this time the club are not that keen on buying another forward," Mourinho told a news conference ahead of Thursday's King's Cup last 16, second leg at Levante.
"Also because it is Madrid it can't just be any player and the situation does not seem very easy to me," he added.
"I only have one striker, Benzema, but we have to deal with the situation.
"I have to get the most out of the players I have available, who are numerous and extremely good.
"It seems we will stick with this group of players until the end of the season."
Mourinho's dilemma is eased by the return to action of Brazil playmaker Kaka, who needed a knee operation after the World Cup and had not played this season.
La Liga top scorer Cristiano Ronaldo, who has flu and will miss Thursday's game, could move up to centre forward, with Kaka playing just behind and Mesut Ozil and Angel Di Maria providing width.
The misfiring Benzema had slipped behind Higuain in the pecking order under Mourinho but has started to come back into form in recent weeks.
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Portuguese Mourinho was also quizzed about the possible exit of Mahamadou Diarra in the January transfer window, and said he would be disappointed if the Mali midfielder left.
Local media have linked Diarra with a move to Malaga, who have money to spend after they were bought by a member of the Qatar royal family in the close season.
"When he plays he makes his contribution to the team," Mourinho said.
"In that sense, it is not easy for him to leave because he has his uses and if nobody is signed it is normal that nobody leaves," he added.
"We hope to be fighting in all competitions until the end and we need all the players we have."
Real, who have not won Spain's domestic Cup since 1993, are virtually assured of a place in the quarter-finals after they demolished Levante 8-0 in the first leg at the Bernabeu. They would play either city rivals Atletico Madrid or Espanyol for a place in the last four.
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