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In the first friendly match under Conte, Chelsea, despite the presence of the likes of captain John Terry, Willian, Diego Costa and Begovic, lost 2-0 to Rapid Vienna.
The former Premier League champions endured a disappointing campaign last season, finishing 10th, and will rely on Conte's fiery touchline presence and work ethic to propel the side back to their winning ways.
"We're buying into what the manager wants us to do, we're working hard to try and improve and work in a different way," Begovic told the club's website.
"It's going to take a bit of time, it's a process, but so far so good and over time we'll get better.
"He (Conte) communicates very well, so he got his message across at halftime and before the game. We expect to work hard, that's part of pre season. We're trying to be very disciplined. The work ethic is very strong."
Former Stoke City goalkeeper Begovic managed just four clean sheets in 17 league appearances for Chelsea last season, and was used largely as a back up to first-choice goalkeeper Thibaut Courtois.
The 29-year-old added that the manager had not yet held discussions about his team for next season.
"He (Conte) hasn't explained too much at all, to be honest," Begovic added.
"It's just about working hard and trying to buy into what he wants us to do. I'm sure those decisions and everything else will come further down the line and we'll see what happens."
