Eden Hazard got his first Blues goal from the penalty spot after Fernando Torres tumbled in the area, and the revitalised Spain striker added the second in first-half stoppage time.
Chelsea have changed their style this summer, but Cole is delighted with how quickly they have gelled.
"We've lost Didier (Drogba), a big powerful presence up front and sometimes we just used to knock it up to him," the England left-back told ESPN.
"But now we've signed some smaller players so we've got to get the ball down a play a little bit more now.
"The second goal today was a great goal for the whole team."
It was Torres' third goal of the season, counting his strike in the Community Shield, and Cole reckons the frontman's new-found confidence is as much a result of Spain's triumph at Euro 2012 as his new role in a Drogba-less Chelsea team.
"Of course it was really hard for him to (only) get that many games (last season)," he said. "But when he did play he worked really hard for the team.
"Now he's the main man, like you say. But he's full of confidence after the European Championships and he scored a great goal today."
Hazard turned in another fine performance to add to his growing reputation since his big-money move from Lille this summer.
"I think he deserves a lot of credit for the start to the season we've had," Cole said. "He's won two penalties, got two assists and now a goal - it's phenomenal.
"We're proud to have this guy in the team and hopefully he can keep doing it."
Hazard added: "I'm very happy to get my first goal at Stamford Bridge."
Chelsea boss Roberto Di Matteo believes all of his players deserve credit for the club's unbeaten start to the new season despite Hazard and Torres grabbing the headlines.
"It's not just them two, they have a good link-up with (Juan) Mata and the other midfield players," Di Matteo said.
"Thanks to the team he (Hazard) has been able to slide in and play very comfortably with the others.
"I know you focus on the goalscorers but I think it was a good performance considering it was our third game in six days. The demand was high playing against tough opposition today."
Di Matteo is pleased, though, that Torres has started to add goals to his game once more.
"He was very important for us last season, maybe not scoring as much but providing and working hard for the team," he said.
"He is a great team player as well but it is great to see him scoring and the second goal I think was terrific play from us."
Di Matteo was without captain John Terry due to a neck injury and the Italian was therefore forced to named a third different central-defensive partnership in succession, but he was pleased with the efforts of David Luiz and Gary Cahill and the defensive performance as a whole.
"That was important today," he said.
"I thought we controlled their threat very well, we didn't concede much to them because if you give space and time to (Demba) Ba, (Papiss) Cisse, (Hatem) Ben Arfa or (Yohan) Cabaye they can hurt you."
Newcastle manager Alan Pardew also acknowledged the performances of both Hazard and Torres.
The two look to be building an understanding at the top of the field for Chelsea and Pardew was very impressed with former Lille man Hazard.
"He is a difficult player because he travels with the ball and buys time and when you have someone who can do that you can time your runs off it," he said.
"He just has a kind of nonchalance about him that marks him out as a great player, every time he got the ball today he made the right decision - he has made a difference to Chelsea."
Torres, who picked up the Golden Boot at this summer's European Championships with Spain, has started the season well and seems to be playing with renewed confidence, something noted by Pardew.
He said: "I thought he was good today, I have seen him a few times up close and that was one of his better games that I have seen, certainly the second goal was a classic goal.
"He had some good moments today and it is good for Chelsea that he is playing well."
Pardew's side travelled to Stamford Bridge on the back of a 1-1 draw against Greek side Atromitos in their Europa League qualifier on Thursday night and the former West Ham boss admitted his side were slow out of the blocks against the European champions, but praised their second-half efforts.
He said: "In the first half I genuinely thought we looked a bit lacklustre and lacked a bit of a spark in that period.
"Chelsea were good in that first half and I don't want to take anything away from them but the goals were bad for us - the goal just before half-time was a killer blow really.
"We really had a go second half, we didn't shut up shop or try and cover our losses we tried to get back in it - so I'm fairly positive about my team."
