The Toffees began the season in great form but have slumped of late - winning one of their last six and becoming Reading's first scalp of the season last time out.
Moyes said: "There's been a couple of games where we maybe should have scored more but we've also got to make sure when we're not scoring that we don't concede.
"Our play has been good enough to have merited more goals and everybody's got to make sure they chip in, the goals have got to come from all departments.
"I'm going out to score and I'm going out to try to win. The best teams get the balance exactly right. But I would still quite happily settle for winning games 1-0, because the job is to win, that's always the priority."
The Canaries, meanwhile, arrive on Merseyside in far more encouraging shape with four wins in their last six, and Moyes is impressed with the impact made by counterpart Chris Hughton.
He added: "I hope they don't play as well as they have been because they've done very well. Chris is doing a good job and they've had some good results recently."
Everton have not been helped by injury problems and will definitely be without captain Phil Neville after he had a knee operation last week.
Striker Victor Anichebe (hamstring) and defender Tony Hibbert (calf) are still struggling but winger Kevin Mirallas (hamstring) and midfielder Darron Gibson (thigh) could play some part.
Gibson's return to fitness is particularly welcome given he has missed the last 10 games, while the Toffees will also be without key midfielder Marouane Fellaini through suspension.
The Belgium international has been one of the players of the season so far but Moyes is confident others will step into his shoes.
The Toffees boss said: "I don't think we need to plan any differently. The team's been playing very well, I know they're in a good rhythm.
"Obviously Felli's been an integral part of that so we'll miss him but we'll try to find a way of winning with the players we have available."
Moyes has also taken the precaution of recalling teenage midfielder Ross Barkley from a loan spell at Sheffield Wednesday as cover.
The 18-year-old has enjoyed a productive two months at Hillsborough, scoring four goals in 13 appearances, and is likely to head back out on loan later this season.
Moyes said: "Because of the injuries I felt we needed to get him back in the squad.
"Ideally I would probably have liked to have left him longer to get more games, and if I don't get him the games I want I'll probably look to put him back out on loan maybe going into the new year. But we'll see how he does while he's here.
"It's really important that we keep his development going and, from what I've seen, he's matured a bit and come on a bit with the games he's had at Sheffield Wednesday. With young players the games make a big difference."