The defending champions won 4-1 in tough conditions on Merseyside, where a bobbly pitch was battered by the wind coming in off the Irish Sea.
The Toffees started brightly, too and City had to be clever to execute an unusually direct game plan, with Gemma Bonner scoring from two set-pieces and Tessa Wullaert converting from a deep cross.
City’s possession-based style was less prominent, but it was a professional performance which Cushing believes was just as impressive as more eye-catching displays.
“The pitch was a bit bobbly and it was really windy, and it was set up for it to be a dodgy occasion for us,” he said.
“But I thought the players were excellent with the way they controlled the game. Everton have got a good team of young players and I think young teams play on enthusiasm.
“If you give them moments where they can grow in enthusiasm, whether it’s mistakes at the back or chances, they’ll grow as a team.
“If you keep the game really professional and don’t give them anything, young players can find it hard to dig deep.
“We had to be more direct tonight and play off the front a bit more to make sure we got the win.
“If you look at the way we played when we went direct, what was pleasing is there was a strategy.
“It was more about playing longer passes and missing out the first line of defence, as opposed to just kicking it.”
With City one of three teams vying for the two quarter-final spots in Group C, Cushing had called on his players to show their clinical side against the Toffees, knowing goal difference could prove vital.
It will come into play should third-placed Birmingham City beat Manchester United in their final game next month and while Cushing is disappointed his side have put themselves in that position, he is satisfied the win over Everton gives us a good opportunity to qualify for the last eight.
“I'm really pleased we've scored four because it gives us a great chance of going through,” he added.
“We need Birmingham to lose. If Birmingham beat Manchester United it will go to goal difference.
“We’ve done everything we can. We’re disappointed we lost to United but we knew we had to come here and get a healthy score.
“We’re on plus seven, so Birmingham have to win by at least four goals, so it gives us a chance.
“If we don’t go through it will be because we didn’t win at Manchester United and we’ll accept that.”