Jordan Suter’s hat-trick, Aaron Hooker-Meehan’s brace and a strike from Owen Cave saw the Swans to their biggest win of the season on Saturday.
The league victory - their sixth of the campaign - lifts them to tenth in Division 1 ahead of the festive fixtures getting underway this weekend.
Their previous best wins had only been by a two-goal margin and their highest scoring game saw a 5-4 victory over Southwick back in September.
On the result, Everett said: “I was really pleased with the win. It’s been overdue as our efforts in recent weeks haven’t brought the points tally I believe they deserve. Saturday was different.
“It was a game we quite simply had to win to move away from some of the teams that have closed the gap below us.
“We took enough of our chances on the day but I wouldn’t say we were clinical. In that second half we created so much and missed easier chances than some of the ones we took. But you can forgive that given that we scored six.”
And Everett has been particularly pleased with Suter, who now has five goals in five games and 12 for the season.
He said: “Jordan has been a revelation this season and his goal scoring feats have been important to us.
“It’s a big step up for him from West Sussex football but he’s adapted well and he will only get better if he wants it. To lose Kelvin (Lucas) early in the game was a blow but it was encouraging to see we still posed a goal threat from others.”
Saturday was a day where a lot of games were either postponed or abandoned but Everett was happy with the way his team played in the horrendous conditions.
He said: “The conditions were pretty bad to start and only got worse but I thought we played them perfectly.
“We hardly made a mistake and we knew that could be the difference on a wet and boggy surface. The goal scorers will take the accolades but it was a team effort and we were solid to give ourselves the platform to go and win the game comfortably.”
The Swans travel to second-from-bottom Midhurst and Easebourne on Saturday and Everett knows what his team have to do.
He said: “Midhurst next for us is another game we simply have to win to keep us away from the teams at the bottom.
“Win that and we move on to Alfold who are flying and it will be tough.
“But we have to start taking points of the sides above us to climb into the top half and I don’t think we have anything to fear from them although we respect their qualities.”