Arsenal won the season-opener 4-1 on penalties as the match finished 1-1 after 90 minutes, substitute Sead Kolasinac cancelling 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.
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.
"For the second time, also if you remember in the final of the FA Cup, there was a controversial decision against us.
"I didn't see the images (of Pedro's tackle)
I didn't see also the yellow card for Willian
A lot of people told me the penalty was clear.
"For sure there is a bit of frustration, but you know very well we have to respect referees' decisions
But sometimes these decisions make you a bit angry."
Conte debated decisions with Madley, but cut the conversation short as "we stay to speak and finish the game at 9pm".
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 season.
"Now in this moment all my players in my squad are important," Conte said.
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 shootout 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.
That gave Arsenal the initiative
Alex Oxlade-Chamberlain scored before Olivier Giroud netted the decisive strike to extend Arsenal's winning record at Wembley to nine straight games, including two in penalty shootouts.
Conte was unapologetic at Courtois taking a penalty.
"Courtois is one of the best players to kick a penalty," said Conte, pointing to Courtois' penalty kicks in training.
Wenger was happy with the performance and result and called for Arsenal to now start the Premier League season well against Leicester on Friday night.
"It's an encouragement, not more than that," Wenger said.
"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."
Alexis Sanchez, Mesut Ozil, Laurent Koscielny and Aaron Ramsey were left out
Sanchez is short of fitness after only recently returning following a break after the Confederations Cup.
Ozil (ankle) and Ramsey (calf) were not risked, while Koscielny is suspended against Leicester and so was omitted here.
Per Mertesacker went off with a facial wound after being struck by Gary Cahill's flailing arm, but should be fine to face the Foxes.
Wenger praised his replacement, Kolasinac, as ready for the rigours of the Premier League.
"He was outstanding," Wenger said.
"Physically he's very strong, naturally
We have players who are pumped up in the gym and players who are born strong
He's the second part.
"He looks to me that he has good talent, as well a very strong, determined attitude, supported by a strong body."
While Conte is looking to recruit players, Wenger is looking to offload.
"We'll let some players go - 33 is too high," Wenger said.
"Too much competition for places is detrimental."
Source : PA
Source: PA