Emery has made a number of changes to the playing style Arsenal were known for under Arsène Wenger and though there have been many teething problems so far, the former Paris Saint-Germain boss has praised his players for their attitude and application since the start of the season.
Emery's side were under the cosh in the first half at the Emirates Stadium, but Cech came to their rescue with a series of fine saves.
This was followed by another superb strike three minutes later as the Pierre-Emerick Aubameyang finished off Ramsey's second assist of the match, to double the goal advantage and put Gunners two in front.
Sunday's 2-0 victory at home to Everton saw Cech in top form as the Gunners recorded a fifth straight victory in all competitions.
Emery's decision sparked claims Cech was on the way out, but the Arsenal captain had other ideas as he rolled back the years with a vintage display. "We are happy with the points".
"Petr, he has a lot of experience and quality", Emery said.
Wenger traditionally used the League Cup as a chance to blood his youngsters, and outgoing club chief executive Ivan Gazidis said when Emery was hired in May that he expected the new manager to have a similar focus on developing academy talents.
"I think 20 times maybe, Cech kept us in the game".
"Leno is calm. He knows now he is working well". Leno will improve and learn with us. "But Bernd Leno is a young goalkeeper and he has a big future here".
Chelsea had won all five of their league matches before the weekend, going toe to toe with Liverpool, who beat Southampton on Saturday to make it six wins out of six.
"We have had a good relationship since day one and enjoy playing together". We have to work.
"It's clear where the player who scored the goal is".
Asked if Lacazette was due to be subbed off, Emery smiled and stayed silent, before replying when asked again: "I think it is not important".