Conte was understandably frustrated after his side were defeated by Arsenal on penalties in the Community Shield on Sunday (6 August) and has spoken about his desire for reinforcements on a number of occasions this summer.
Their struggles in the transfer market was reflected by the quality of the substitutes named by Conte for the pre-season curtain raiser against Arsenal. And Sutton, who endured an ill-fated 12 months at Stamford Bridge between 1999 and 2000, thinks the Italian has little say over the club's transfer dealings and is particularly frustrated by Matic's departure to Manchester United, who are seen as contenders for the Premier League title.
"I don't think they have enough strength in depth," Sutton said on Match of the Day. "They've let too many players go. I don't think Antonio Conte's happy. He didn't want [Nemanja] Matic to go to Manchester United so there's question marks over whether he has the power at Chelsea."
Sutton's fellow pundit and former Liverpool defender Mark Lawrenson echoed the former Celtic forward's sentiments, saying that Conte will be demanding Michael Emenalo to act fast in what's left of the transfer window as he bids to maintain Chelsea's status as champions and avoid a repeat of the season they had under Jose Mourinho a couple of years ago.
"I think he'll be knocking on the chief executive's door at Chelsea and saying 'look we lost that game we definitely need some players' - otherwise they are gonna struggle a bit." Lawrenson added.
Chelsea have spent close to £150m already this season on the likes of Alvaro Morata and Tiemoue Bakayoko but they missed out on their perceived top target Romelu Lukaku, who joined United in a deal worth £90m.
Conte is desperate to add depth to his squad in order to compete both domestically and in Europe and is reportedly targeting Danny Drinkwater, who is believed to have told Leicester Citythat he is keen on a switch to the capital.
The Blues are also pursuing Southampton captain Virgil van Dijk and have reportedly submitted a £50m bid for the Holland international, who has his heart set on joining Liverpool.