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."
Media playback is not supported on this device
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."

Notts leg-spinner Imran Tahir led the recovery with 7-112 as Somerset were all out for 437 - a lead of 36.
Resuming on 244-3, South Africa international Tahir claimed six of the seven Somerset wickets to fall on a scorching day - including Trescothick, who added 101 to his overnight 117.
Notts lost Steven Mullaney and Michael Lumb early, before closing on 58-2.
Trescothick, who equalled Somerset's record for the most first-class centuries with his 49th on Monday, was in wonderful form once again despite stifling temperatures.
The 40-year-old brought up his double century off 323 balls with a trademark cover drive off Samit Patel - his 31st boundary - before he was the last man to go, chipping Tahir to cover.
Somerset looked set for a much bigger lead as Trescothick and Jim Allenby's hundred partnership took them to 379-4 and within 22 of the hosts.
But once Allenby was bowled by Patel for 63, Tahir tore through the rest of the batting order as Somerset lost their last five wickets for 37.
The procession of afternoon wickets continued in Nottinghamshire's second innings as Craig Overton pinned first-innings centurion Mullaney lbw and Allenby bowled Lumb without scoring in the next over.
Jake Libby and Brendan Taylor batted out the final hour to give Notts a lead of 22 at stumps.
Chelsea boss Antonio Conte says he is "not worried" by the club's relative lack of signings this summer.
[NEXT_CONCEPT]
Somerset opener Marcus Trescothick hit a superb 218 before Nottinghamshire fought back at Trent Bridge.