The Toffees have only picked up seven points from the first seven Premier League games this season, and this disappointing form has led to manager Ronald Koeman having to be publicly backed by owner Farhad Moshiri last week.
Everton received £75m this summer for the transfer of Romelu Lukaku to Manchester United, and Koeman decided to reinvest that money back into the transfer market, but signing players such as Gylfi Sigurdsson from Swansea for £45m and Keane from Burnley for £25m.
This high expenditure, coupled with disappointing on-field results, has led to increased pressure on the Dutch coach and his players, and centre-back Keane fully acknowledges that performances this season have been below par.
"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.
"I did not think that was the case (against Burnley). We just need to show that bit of quality and, hopefully, we will do that soon.
"It is a great set of lads here and the staff have been brilliant with me. It has not been the best of starts with results but I am enjoying my football and, hopefully, there is more to come."