Coleman opened the scoring with a stunning strike on Sunday as the Blues beat Swansea 2-1 in South Wales.
There was a late scare for the Toffees when Bryan Oviedo scored a second-half own goal, only for Ross Barkley to step up with a stylish finish of his own to seal all three points for the visitors.
Victory over the Swans means Everton are now unbeaten in 10 games and Coleman believes they can go on to underline their top four credentials over the Christmas period.
Speaking to the Liverpool Echo, he said: "Of course we want to be up there with the best teams and we deserve to be where we are because of our form.
"We're not pulling away from sides yet because all the top teams are winning but we're hanging in there and that's what counts.
"It's crazy. You keep looking one game at a time but we're going into two home games and we're going into it with confidence. We'll keep winning games and see where we go."
Despite collecting all three points at the Liberty Stadium, Coleman believes Everton have much more to come having faltering mid-way through the game.
"We knew that it was going to be tough," he added. "They're very good with the ball and they're good at closing you down, and in the first half we didn't get into it at all.
"Throughout the game I don't think we played as well as we can. But we got the win nevertheless which is always a good sign."
Barkley's winner dominated the Monday morning headlines and Coleman also took the opportunity to add to the plaudits, as well as giving praise to Gareth Barry and James McCarthy for their midfield efforts.
"It was a fantastic goal from Ross," he said. "We see it from him every day. He's a top player and he's only going to get better, but he's also a grounded lad who loves his football. We're lucky to have him.
"Then we've got the likes of Gareth Barry in the middle who's seen it all and his experience is great.
"When we're under the cosh, he helps us bed down, and then with James (McCarthy's) energy he plays a bit part too which you saw with the free-kick for Ross' goal.
"When it's not going so well, we have players who can relax us, and we're full of confidence now.
Coleman's strike was his fourth of the season and the right-back admits he is brimming with confidence in front of goal.
"If you ask any striker or midfielder who scores goals, if they score one week they feel like they're going to score the next," he added. "That's the way I am at the minute.
"I've been in the right position a few times and scored and it lifts your confidence. Maybe if I was missing them, I wouldn't have taken that shot on but I did."