The Italian also hints at frustration with the squad depth of the Premier League champions after they lose on penalties to Arsenal at Wembley Stadium.
Chelsea manager Conte angry by decision to send off Pedro in Community Shield
Chelsea manager Antonio Conte was "angry" after Sunday's Community Shield loss to Arsenal at Wembley.
Arsenal won the season-opener 4-1 on penalties as the match finished 1-1 after 90 minutes, substitute Sead Kolasina ccancelling out Victor Moses' opener for Chelsea.
Conte was denied a double in his first season as Chelsea boss as Arsene Wenger's Gunners won May's FA Cup final in controversial fashion.
An offside dispute and Moses' dismissal for diving was the reason for his angst on that occasion and on Sunday Conte felt aggrieved once again.
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The Premier League champions had Pedro dismissed for a tackle from behind on Mohamed Elneny and referee Bobby Madley ruled Willian had dived instead of awarding the player a penalty.
"There is disappointment to finish for the second time with 10 men against Arsenal," the Italian said.
"You know very well we have to respect referees' decisions. But sometimes these decisions make you a bit angry."
Conte, who has spoken of the need for Chelsea to add players to the squad, issued terse responses to questions which he has faced repeatedly of late.
The first sign of tension was when he was asked about the importance of Charly Musonda, who came off the substitutes' bench after being a perennial loanee in recent seasons.
"Now in this moment all my players in my squad are important," said Conte, whose side begin their Premier League title defence against Burnley on Saturday.
Next the former Juventus and Italy boss declined to answer when asked if his squad was ready to challenge in all four competitions this season.
Conte was then asked what strikers Michy Batshuayi and Alvaro Morata can offer that exiled striker Diego Costa cannot.
He added: "I hope in the future to have a different question... 'if there is necessity to improve our squad', about our strikers.
"I replied. My reply is always one, otherwise it means I was telling you a lie."
An English football first took place at Wembley as the 'ABBA' penalty shoot-out system was deployed.
Based on the format used in tennis tie-breaks, the team taking the first kick in each pair of kicks alternates.
Goalkeeper Thibaut Courtois took Chelsea's second kick, seeking to equalise, and blasted over before Morata, the substitute striker, fired wide.
Alex Oxlade-Chamberlain then scored and Olivier Giroud netted the decisive strike to extend Arsenal's winning record at Wembley to nine straight games, including two in penalty shoot-outs.
Wenger was happy with the performance and called for his players to start the Premier League season well and create a positive atmosphere around the club.
The Frenchman, who signed a two-year contract extension after a record seventh FA Cup win, admitted the uncertainty over his future last season may have resulted in ill-feeling.
Wenger, who is nearing his 21st anniversary as boss, said: "It's down to us to put a positive atmosphere around the team.
"A lot was created by my own situation. Maybe I made a mistake.
"Overall I believe that it's down to us. The trend has always to come from the team.
"We had some bad starts recently, the last four years, in the first game of the Premier League.
"But we had the intensity in the games in our preparation that is needed to be ready."