Manager Roberto Martinez said Romelu Lukaku was "unplayable" and labelled Ross Barkley a "diamond" after the pair grabbed the goals that helped Everton to
Everton were 3-0 up at the break thanks to Lukaku's double and a strike from Barkley, 19, before Newcastle hit back through Yohan Cabaye and Loic Remy.
He said: "For a number nine to have that awareness, Lukaku was unplayable.
"Ross is a diamond of English football, but he still has a long way to go."
Barkley made his Everton debut two years ago, in a 1-0 defeat by Queens Park Rangers, but only made a handful of appearances after that before spending time on loan at Championship sides Sheffield Wednesday and Leeds.
However, he has developed into an Everton regular this season with a number of impressive displays, culminating in him earning his first England cap last month with a substitute appearance in the 4-0 World Cup qualifying win against Moldova on 6 September.
"I was over the moon because I've dreamt about that moment [scoring at Goodison Park] since I was a kid," Barkley told Everton's club website.
"It was important to get the second goal and give us an extra platform. To get three before half-time was impressive and gave us a big boost.
"It was a great team performance. We were playing it about nicely and everyone was feeling confident on the ball."
Lukaku, who Martinez said "looked at home" in his first league start for the club since arriving on loan from Chelsea on transfer deadline day, scored after five minutes before he supplied the pass for Barkley to fire home Everton's second.
Lukaku then took advantage of two errors in the Newcastle defence to prod in a third. The Magpies improved after the break and reduced the deficit, first through a stunning strike from Cabaye before Remy added another with a minute of normal time remaining.
The former Wigan boss added: "Barkley is the sort of player who controls things in midfield, and that is unusual in a player his age. I think he is an exceptional ambassador, not only for Everton but English football as a whole.
"It is almost a question of keeping him away from the training ground because he is so eager to improve himself."
He added: "It is natural [to fade], I don't think we could carry on with the tempo that we managed in the first half.
"I was really disappointed for the defenders and team, they did not deserve to concede the two goals. But overall, it was an important win and the chemistry between the players and the crowd was good."
Newcastle manager Alan Pardew said his side's first-half display was "disturbing".
"The goals were poor in the first half. Definitely we have got to be better than what we are," he said.
"We've got goals in the team and we showed that, but we've got to tighten up.
"Nothing went right for us and the inconsistency being shown was disturbing at one point, but in the second half we got some balance in the team and came out with some pride, and almost at the end got more than that."