He added: "I believe the quality of the game was very good".
According to Transfer Market Web, the 23-year-old Italy global has been on Wenger's shortlist for over a year now, but was overlooked last summer as he chose to sign Shkodran Mustafi last summer.
Key players Alexis Sanchez and Mesut Ozil are still yet to commit to the Gunners beyond their current deals, which expire in the next 12 months, and Wenger conceded the uncertainty surrounding his own situation may have eked into the dressing room.
Last season was by far the most hard of Wenger's 21-year tenure as manager, with Arsenal's on-pitch travails exposing him to furious protests from sections of the club's support.
"Overall I believe that it's down to us.
He couldn't practice and he couldn't play", Wenger told a news conference.
"The Premier League is the most competitive league in the world and Arsenal are one of the best clubs in it, year after year they've shown their consistency", said Shakespeare.
GETTYOlivier Giroud's long-term future at Arsenal remains under threat
Chelsea lost friendlies to Bayern Munich and Inter Milan, and were defeated on penalties by Arsenal in Sunday's FA Community Shield.
The 26-year-old set Arsenal back an initial fee of £46.5 million ($60.3 million, 51.5 million euros) and is expected to lead the line, flanked by Sanchez and Ozil.
He has said he intends "to focus completely on the Premier League", but if such an approach fails to yield a title challenge, he can expect the protests to ramp up quickly.
Kompany was named the Premier League's player of the season that year and was also included in the PFA Team of the Year - one of three occasions he has earned that accolade.
As far as the wing-back positions are concerned, the likes of Bellerin and Kolasinac will probably start. I remember watching him at Bournemouth last season and he looked angry. Danny Drinkwater (thigh) and Robert Huth (ankle) are also out. We had some bad starts recently, the last four years, in the first game of the Premier League.
The England worldwide has struggled to secure a regular first-team place since joining the Gunners six years ago, but Wenger believes the former Southampton winger is finally starting to fulfil his potential.