It was by no means an ugly win on Merseyside, where a Steph Houghton free-kick was the difference, but City were required to show resilience in defence after several spurned chances gave the hosts hope they could nick a draw.
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Cushing admitted he was frustrated by a number missed opportunities but was full of praise for his players' faultless work ethic and desire to win.
“If we don’t take our chances it leaves the game open for a team to try and nick a 1-1,” he said.
“The last 15 minutes were probably Everton’s because we allowed them to throw high balls into the box from wide areas.
“We had to rely on our resilience and our strong defensive ability to get through to the win.
“To be a top team, when things aren’t going your way, you have to bring that other side of your game out.
“I’m pleased. This is the end of a difficult period of games and getting the win was the main objective.”
That driving rain water slowed the run of the ball in wide areas provided City with another obstacle to overcome.
Last season’s double cup winners were forced to abandon our usual expansive approach and take a more direct route through the middle of the pitch.
It played into Everton’s hands and while Cushing believes the game should have been put beyond doubt, he had sympathy for his players.
“I thought our build up play in the first half was very good and we created a lot of opportunities,” explained the 34-year-old.
“The water killed our build up a bit.
“It stopped us being able to play across the pitch, so we lost the width and had to go direct.
"That’s not our game and it helped their press."
The sight of Lauren Hemp haring down the left flank provided the boss with an additional positive in victory.
The 19-year-old was introduced from the bench in the 70th minute for her first appearance of the season after missing the opening games due to a shoulder injury.
She nearly marked her return with an assist, too, had Pauline Bremer not headed wide and Cushing is delighted to have her back in the fold.
“I’m really pleased to get Lauren Hemp back on the pitch,” he added.
“She was going to start the game, but the team’s been playing well. She went on and did well.
“We’re hoping to have more players back after the international break, so the competition for places will be there.”