The Toffees have endured a torrid start to the season and currently find themselves in 16th place in the table, with just two wins from their opening seven games in the Premier League.
With the Everton hierarchy splashing the cash over the summer to bring in the likes of Swansea's Gylfi Sigurdsson and Keane from Burnley, it has been tough for the Merseysiders, who were tipped for great things this term.
England centre-back Keane feels the side must focus on improving ahead of their next Premier League outing against Brighton on the south coast on October 15.
"I think everyone expected more than we have given so far: the players and the staff, not just the fans," he said. "We know we have been disappointing as a team and need to improve.
"Expectations from fans is one thing - but the main thing is what we expect of ourselves. And in a few games this season we have fallen below those standards."