The Group Eight leaders host Bulgaria on Wednesday where a win would put them four points clear of second-placed Ireland and on the brink of World Cup qualification.
However, they needed two own goals from Kakha Kaladze to win in Georgia on Saturday and recent poor performances have led fans to count down the days until Juventus forward Amauri gains an Italian passport.
"One player is not the solution to the problems of the team," fellow striker Gilardino told reporters.
"Amauri is really good but now what counts is the group and even if he is called up he will not have a place assured."
Gilardino was left on the bench in Georgia where Vincenzo Iaquinta and Giuseppe Rossi played upfront and substitute striker Fabio Quagliarella staked a claim for a starting spot.
Coach Marcello Lippi has said he will consider Amauri but bureaucratic delays mean the 29-year-old is unlikely to be available before the end of the qualifying campaign.
Inter Milan midfielder Thiago Motta, born in Brazil, might also be eligible for the Azzurri and defender Giorgio Chiellini would welcome players who did not grow up in Italy.
"In the rugby team for example there are lots. We are not a closed group. If Amauri or Thiago Motta came there wouldn't be problems," said the Juve defender, who was looking forward to playing at his home stadium in Turin on Wednesday.
Media reports say Juve team mates Fabio Grosso and Claudio Marchisio will come into the side against the Bulgarians.
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