The Italian was asked about the Pulisic's signing after Wednesday's draw against Southampton at Stamford Bridge.
It was the second straight home match in which Chelsea failed to score.
The tepid and one-paced performance raised more questions about the need for a top-class striker on a day they splashed out £58 million (S$99.7 million) on Borussia Dortmund midfielder Christian Pulisic.
At present, Higuain is on a two-year loan deal with AC Milan and the Blues are apparently reluctant to discuss terms with two separate clubs in order to lure the marksman to the Premier League. I think we need something different for characteristics.
He made it clear the responsibility for new signings lies with owner Roman Abramovich, saying: "It depends on the board, not on me". "[Hudson-Odoi] I think in this season played six, seven official matches in Europe, so I think that he has to be lucky".
"We have to try to solve the problem of the last 15, 20 metres". In the last few matches we were in control against every team but at the moment it's not easy for us to score the first goal.
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Reports suggest that the West London club have cooled their interest in the former Real Madrid player. Sarri told the press after last nights game.
The boos rang out at full-time as Cesc Fabregas, who came on as a 68th-minute substitute for his 500th club appearance in English football, was waving to the home fans.
AC Milan are anxious about losing him and are preparing for a tough next few months as more clubs look to join the chase for Kessie.
Chelsea is now fourth in the table, three points ahead of Arsenal and six up on Manchester United for the last Champions League spot.
The 2016/17 champions missed a chance to close in within a point off third-placed Manchester City who have a game at hand against league-leaders Liverpool.