The Blues have signed four players for a combined £129m, but have seen a greater number leave, including John Terry and Nemanja Matic.
Their Premier League title defence began with a shock 3-2 home defeat by Burnley on Saturday, during which Gary Cahill and Cesc Fabregas were sent off.
"The club are trying to do their best," said the Italian.
"I am not worried, I am ready to fight with these players.
"I repeat: It is important for us to concentrate on our work, to be focused every day in training and to try to work in our best way. No excuses."
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As well as defender Terry and midfielder Matic, Chelsea have sold Asmir Begovic to Bournemouth, while last season's top scorer Diego Costa has been told he is free to leave.
The recruitment of midfielder Tiemoue Bakayoko from Monaco, striker Alvaro Morata from Real Madrid, defender Antonio Rudiger from Roma and former Manchester City keeper Willy Caballero fills the gaps vacated by this quartet.
But Conte has made no secret of his desire to recruit more players to strengthen his first team for a season that sees the addition of Champions League matches to their fixture list.
Having also sold Nathan Ake to Bournemouth and loaned fellow defender Kurt Zouma to Stoke, the suspension of Cahill will further deplete Conte's resources.
Equally, Fabregas' ban deprives him of another midfielder, with Bakayoko, Hazard and Pedro all out injured.
Conte felt Cahill's dismissal was pivotal to the outcome of Saturday's game against Burnley, with Chelsea 3-0 down at the break following two goals from Sam Vokes and a Stephen Ward strike.
A debut goal from substitute Morata and a late David Luiz finish gave them hope, but Burnley held on for the win.
"The red card [for Cahill] was the key moment," Conte told BBC Sport. "We started well with good intensity and were dominating the game. Then the game changed. We lost our heads too easily and we need to reflect on this situation.
"If we are able to stay in the game, then anything can happen in the second half, but instead we conceded three goals. In the second half, my players showed great will to try to change the result."
Chelsea boss Antonio Conte says he is "not worried" by the club's relative lack of signings this summer.