Andre Gray scored his first Premier League hat-trick and his manager, Sean Dyche, expects the 25-year-old Burnley striker to get even better in 2017.

Burnley equalled their joint-largest Premier League victory by demolishing Sunderland, whose woeful defending was typified by Papy Djilobodji’s dire afternoon, as Gray scored three times inside an hour.

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A seventh home victory of the season was rounded off by Ashley Barnes’ penalty as Burnley moved up to 11th, nine points clear of 18th-placed Sunderland, who claimed a consolation through Jermain Defoe.

The win came five days after Gray’s late winner against Middlesbrough and the forward, who missed four games earlier in the year owing to a Football Association ban for historical homophobic tweets, maintained his excellent form.

Last year’s Championship player of the year helped Burnley win promotion and Dyche believes there is more to come from the former non-league striker. “He’s still a work in progress and he can only add to his confidence level and belief playing at this level,” he said. “I don’t think any player just arrives in the Premier League and you just roll out there and learn instantly, some but not many. It takes time. I’ve said about people like Steven Defour still adapting to what the Premier League offers and Andre’s the same – he’s had an unbelievable journey in the last four seasons and he’ll continue to learn. All of our players are. He’s got that fearless streak in him if he misses. He’s got a real firm mentality.”

Gray also had a helping hand from Djilobodji, who was sucked into an aerial duel with team-mate John O’Shea for the striker’s first goal before losing him for the second and third.

An early injury to Lamine Koné, which forced O’Shea in alongside Djilobodji hindered matters, but David Moyes fumed after Sunderland were undone by routine attacks.

“We couldn’t really cope with old-fashioned English style balls down the channel, balls forward, balls over the top,” the manager said. “We didn’t deal with it well. We didn’t give ourselves a chance defensively. We didn’t cope with anything well at all.”

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Moyes added: “It was a poor performance – really, really bad – and defensively we were all over the place. The players have to take responsibility as well as me. You can ask me questions about myself and my future, that’s fine. We’re in the bottom three, I know that.”

With Victor Anichebe also picking up a hamstring injury, Sunderland enter a new year with little reason for optimism. “We have always said if we could do we would, but everyone knows we have got restraints,” Moyes said of possible signings. “I think with what we have got, of course we need help. So let’s hope maybe something happens and we can do that. Ellis [Short, Sunderland’s owner] is saying let’s see what’s out there, and maybe we can do something.”

Dyche will see little reason to spend greatly. At the end of 2016, when his side won 14 of their 22 games at home and lost only three, the Burnley manager reflected on a memorable 12 months.

“It’s certainly a very strong way to finish off a very important calendar year,” Dyche said. “We got promoted and were almost instantly written off. I think it’s a strong mentality to keep looking beyond that and saying what are we about, what can we focus on and what can we deliver in order to win games.

“There’s a nice humility about us because we know we’re not the real deal, we know we’re not just going to run through the Premier League and run over everyone but there’s an inner belief.”