The 5-2 mauling by Arsenal on Sunday has piled pressure on the Toffees boss, whose future is in doubt after overseeing just two wins in 13 matches in all competitions this season.
The loss was the Toffees’ fifth defeat from their opening nine Premier League games and leaves the club languishing in the relegation zone with just eight points.
However, Everton defender Keane has backed Koeman insisting the players must shoulder a great deal of responsibility.
“The lads were devastated in the changing room. We knew it was a big game for the club,” he told evertontv.
“The lads are low on confidence. I don’t think that was the case early on but as the goals went in it happened more and more.
“I think it is down to us at the end of the day, the manager can only do so much.
“We have 100 per cent belief in the manager – we have done all season – and we hope we can get this right for him.
“We feel like we have let him down as a bunch of players and we are working hard to sort it out.
“It is not happening at the minute so we have to try different things to sort it out quickly.”
Koeman says there can be no excuses for the club’s slide into the relegation zone, but believes the Everton players are still behind him.
He told Sky Sports: “That’s the feeling that I have [players back me] but I don’t know. With every manager working with 28-29 players you cannot work with all of them being happy but there’s still enough understanding. That’s my opinion but I don’t know.
“We played nine Premier League games. We played against the first five of the Premier League last season and this is not a good position for Everton.
“I’ve been working in football for a long time so I know what can happen.”