The Toffees were beaten 3-0 at home to Wigan last Saturday when they left the field at Goodison Park to the sound of loud booing from the dejected Everton fans.
The Merseysiders now entertain Manchester City in the Premier League at Saturday lunchtime and Moyes wants an immediate response from his players.
Everton are currently seventh in the table, two points adrift of Arsenal in fifth and Moyes said: "I think the expectations have risen even higher. The team's performances this season have been the best football we've played in my time.
"The quality of the players, the style they've played in, the way we've gone about our job has rightly so put Everton at a level where the expectancy was that Everton have got a chance of top four, Everton have got a chance of winning one of the cups.
"When that doesn't happen then it's a big shock and it was a big shock to us as well, we didn't expect it (losing at home to the Latics."
As for recovering their confidence in time to face City, he added: "You can see the way they've spoken this week, that they're saying they're ambitious to finish as high up as they can, qualify for Europe if they can.
"Well that's the same as the manager and that's what we're going to try to work towards."