Moyes said: “There is nobody with bigger expectations for this club than me, and yes, they have been raised over recent years which means there is some pride and relief that we have finally made this next step up to European level.
“The supporters, too, have those expectations and it is up to us to meet them. But I expect David Moyes to be managing teams in Europe, I expect to have winning teams and good footballing teams.
“That is my job. If you want to be a great leader then you have to have big expectations and I want to be a great leader of a great football club.”
He added: “We have been trying to bring it back to a high level. It is more than six years or so without any real success here.
“We are just trying to get this club back on a proper footing for a club of this size. I believe there will be a bigger and better Everton in the future, this is only the start.
“We got very close to it two years ago. We are a big club and not in Europe. In perspective we have only got through the qualifier, we have not won anything.
“We have not done anything. But this is the beginning of where we want to go. Blackburn, Bolton, Middlesbrough have all been in Europe and reached cup finals. We have had to get over this first hurdle.
“We have not managed that in the Champions League, UEFA Cup and our own cups. We have had three top-seven finishes in five years, so this is the next step.
“My relief was probably because of how the supporters felt after we lost in Bucharest, it hurt them and it hurt me. It took me and the team a long while to get over that disappointment, so I was well aware that getting knocked out of Europe can effect your league form.
“That was why it was important. They gave us as many problems as Arsenal, Manchester United or Chelsea. That is why it was a great result.”
