Sean Dyche says he is encouraged by his Everton side's improving ability to dig in and grind out positive results following the 1-0 FA Cup third round replay victory over Crystal Palace at Goodison Park.

The Blues set up a home tie with Luton Town in round four of the competition, courtesy of Andre Gomes' sublime free-kick just before the half-time interval on Wednesday.

It was a night Everton weren't at their "cohesive best", according to Dyche, but the manager believes the quality of finding ways to navigate through those moments - three days after holding high-flying Aston Villa to a goalless draw - is a crucial characteristic his players must continue to show when necessary.

"I'm pleased with three clean sheets on the bounce, unbeaten in three, of course, and a win - in the Cup but we still want to win, get that winning mentality and maintain it," Dyche told evertontv. "We weren't by any means at our best but we've had very dominant performances where we haven't won games so it's pleasing to see one of those 'maybe' performances, where we still got in some great areas, turned into a clean sheet and a win thanks to a fine goal from Andre.

"There were some good individual performances [against Crystal Palace]. We never quite found our really fluid moments but there were some good individual displays. 

"There is a lot made of cup competitions in modern football and it is different, there are no two ways about it. The energy is different on and off the pitch. It's a strange thing to explain but it's not just us, it's across football. Until the latter stages of the cups, you see these odd results and odd performances.

"I didn't think we were bad but it was a flat performance in the first half, I would say, apart from a fine moment of quality. In the second half there was a little bit more purpose in our play without finding the final killer moments.

"But it bodes well when you're not quite on-song and you win 1-0. That's a good sign.

"The clean sheets are important as well. Against a very good Aston Villa side, I said afterwards that if we can't find a way to win then we don't lose it - and I think that mentality has improved no end here."

The Toffees now face a free weekend as part of the delayed winter break and Dyche says his players and staff will be given a short period of time off to recharge - physically and mentally - ahead of the FA Cup fourth round clash with Luton Town at Goodison on Saturday week.

The Blues boss also hopes the break will help a handful of players facing injury concerns, with Abdoulaye Doucoure and Seamus Coleman both missing the Cup replay with Palace due to hamstring issues.

"We have a thinnish squad and a couple of injuries, with Doucs, who is unfortunately injured and we're not sure how long for yet, Seamus probably lesser so but we don't want anymore injuries," added Dyche.

"Youngy is on the way, on the other hand.

"They'll get a few down days now, obviously with no game at the weekend, then we'll ramp it up ahead of the next one.

"It's about balancing the squad out, finding ways of getting what's best for them as individuals and how they link into the group is important. We've had signs of that and it's good to see the guys who haven't been playing as regularly getting minutes and getting fitter and sharper."