However, he stated that the club's current situation means that avoiding relegation is all they can hope to achieve.
Dyche told Everton's YouTube channel: I've never questioned the fans: good, bad or indifferent, I don't think actually I ever have because you know I was a fan when I was a kid. Believe it or not, I'd support Kettering Town, my local side, but everyone deserves the right to have their opinion, I haven't got a problem with that.
Generally, we've played our part, they've played their part without a doubt. There's time when they (Everton's squad) get questioned, that's part of being footballers, that's part of being a football manager, part of being a player, part of being a fan.
I've got no problem with that at all because generally the fans here have been absolutely amazing and continue to be so, they travel everywhere. The biggest one for me was Crystal Palace away, it was amazing, the FA Cup (third round) we had four thousand there.
I've been in football a long time and I was like wow, I haven't seen that for that type of game very often in my life. So total respect goes out to the fans and are they deserving more?
Possibly, over the last number of years. But we are a work in progress, we are where we are.
We are reality bound and I've tried to inform the fans. I thought the underlying message when I got here not to me but to the club was 'just tell us the truth' as they called it, that's what came to me.
I've tried to be as truthful in all of my business as I can. You can't please everyone all the time, I know that from football, but at the end of the day I'm trying to say: 'Look, you wanted the truth, I think we've done some work to get to a more truthful position, not just in our words but the way the team are performing, wearing the shirt with pride, the work ethic, the belief in what they're doing,' I think we've come some way with that."