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Seamus Coleman believes three points at the weekend was a just reward for the squad's hard work in the week with newly-appointed boss Sean Dyche.
It was a dream start to the manager's reign as Everton manager, with the Blues triumphing 1-0 over title-chasing Arsenal.
While Coleman was delighted to get off to a winning start under Dyche, he believes the squad will only get better in the coming games.
Speaking with Viaplay and quoted in the Liverpool Echo, Coleman said: "You don't just get three points by luck in this Premier League.
"We'd more than enough deserved those points because of the chances we had but in terms of a script, yes, the manager has worked hard on us in training, which positions to be in and when they have the ball on one side of the pitch, to tuck in and make it tight. You don't get those three points without doing your homework.
"A new manager comes in and everyone starts from zero again and gets an opportunity. It's been a tough week but we're happy with how it went.
"It's very cliched but [we must just concentre on the] next game. Three points, enjoy the feeling because we've not had it in a while and next game."
One of the standout performers on the day was Amadou Onana, who caught the eye of Dyche in the home dugout at Goodison.
However, speaking to the media afterwards, the manager insisted the Belgian still has a lot to learn and revealed he would be contacting former Premier League midfielder Steven Defour to pass on advice.
Quoted in Liverpool World, Dyche said: “He has got a lot to learn. I think he is a talent [but] the ugly side of the game he has to learn. I had a very similar process which I spoke about, I had a bit of fun with him, Idrissa [Ganna Gueye] and [Abdoulaye] Doucoure and I said I am getting you to speak to Steven Defour and we will be doing that.
“He said, 'Steven Defour, I know who he is' and I said, 'So do I and when we speak to him next week he will teach you about what the requirements of the Premier League are'.
“He is a young man who is learning. He has come in here with real talent and is fantastic physically and we will get him fitter and sharper and teach him the ugly side of the game and to be a more complete player.
“He has a lot to offer but has a long way to go to become a complete player and Steven will help me possibly educate him. He is a well-respected international footballer for Belgium and he will rub off on him. If he doesn't, I'll rub off on him."