The Italian guided the Blues to the Premier League title in his first season in charge, having sat top of the table for most of the campaign - partly in thanks to their absence from European competition.
Having lost John Terry, Nathan Ake and Asmir Begovic, Conte has allowed three reserve players to leave the club, while Antonio Rudiger and Willy Caballero have been signed.
With the Blues are preparing to compete on all fronts next season, though, Ancelotti believes they need to do more to improve the quality and quantity of the squad.
"The first thing, the most obvious, is that Chelsea will replace Leicester in the Champions League and the difference in quality seems evident to me," the current Bayern Munich boss told Corriere dello Sport.
"But the Blues must step forward: last year Conte won the Premier League by using the same players all the time, that team had great quality and coped well, having to compete only in the league.
"Now for the Champions League he has to buy a lot and well, he needs other players of a higher level.
"The competitiveness will increase next season for a number of reasons: the return of the big Brits like Chelsea and Manchester United, the desire for redemption from the likes of Barcelona and Bayern, Juve's desire to finally raise that cup after losing so many finals, and above all the idea of Real Madrid winning a third in a row.
"The goal for all these teams, and also Paris Saint-Germain, is the semi-finals."
As well as Chelsea, Ancelotti is seeing another of his former sides succeed in Real Madrid, with his former assistant, Zinedine Zidane, leading them to a second consecutive Champions League crown last season.
And the former AC Milan star and coach believes it is heavily down to the Frenchman's quality.
"Zizou has done something unthinkable, no one has ever been able to win two Champions League titles in the first two years of their career," he said.
"It was great. Those victories are the result of his abilities, the extraordinary quality of the players at his disposal and the relationship that unites that group with the coach, and there is a strong bond between them."