Moyes also says Everton's recruitment team is now set to be bolstered.
He told the Liverpool Echo, “Look, it’s always been this way, especially in the summer window. The January one is quite short and it’s over and done quite quickly but I think the summer one has always been a situation like that.
“You’re backwards and forwards with players, things can change with injury or just with how it is. We’ve got to try and start to rebuild again.
“We’ve just left Goodison and we have to start the new story of how we build ourselves up at the new stadium, how we can become a side that is more competitive against the big teams again. When I left, I felt as though we were competitive against most of the top sides at that time and I think we’ve got to try and attempt to get to that.
“I don’t think that can be done immediately. Well, it certainly can’t be done immediately, that’s for sure.
“James Smith is joining us very shortly, who has been head of recruitment at Manchester City, so we’re hoping that he comes back more experienced and with more knowledge, which will help us going forward.”