The former Toffees defender is enthused by the captures of Tom Cleverley and Gerard Deulofeu, but is wary of Ramiro Funes Mori.
Champions Chelsea pursued the highly rated defender throughout this summer, as covered by Sky Sports, with Jose Mourinho’s side having several big-money bids rejected for the youngster.
Stones also reportedly put in a transfer request, something that was also quickly rejected by manager Roberto Martinez and chairman Bill Kenwright - as reported by the club's official Twitter account - who resolutely refused to sell one of their prized assets.
And Keown says that will have felt like winning a trophy, claiming the fans will be delighted with the stance Martinez and Kenwright took in the saga.
“The biggest deal of the summer for Everton was hanging onto John Stones,” he told the Daily Mail.
“He is such a talent and I always felt he was best served by staying on Merseyside and playing first-team football. Keeping him almost felt like winning a trophy for that club and the fans must be delighted at the stance of Bill Kenwright and Roberto Martinez.”
Enthused by Cleverley and Deulofeu, unsure about Funes Mori
The Blues were mostly quiet in the transfer window, leaving it late to secure players after two early deals for Tom Cleverley and Gerard Deulofeu.
They then added striker Leandro Rodriguez, before defender Ramiro Funes Mori and winger Aaron Lennon completed deals on deadline day to further bolster manager Roberto Martinez’s options.
And Keown thinks Cleverley in particular is a sound addition, but says there are mixed reports about their new Argentine defender.
“In terms of players they brought in I think Tom Cleverley is a sound addition and Gerard Deulofeu is a player I like,” he added.
“I’ve heard mixed reports on new defender Ramiro Funes Mori so that could be a bit of a gamble but Everton needed bodies in defence, especially after releasing Sylvain Distin and losing some key players to injury.”