"There's no need for fans to worry. We made sure the club wasn't reliant on any one individual," Carter told BBC Sussex and BBC Surrey.
"We had agreements that should anything happen, the club wouldn't suffer. The club continues to thrive."
She added: "We'd known about his illness for some time and Bruce hadn't had much to do on a day-to-day basis for quite a few months.
"Bruce was very passionate about the club. Crawley Town was his life.
"We are now doubly determined to finish what we started at the beginning of the season and ensure Bruce's dream of playing in the Football League."
Reds manager Steve Evans says Winfield has laid the foundations for Crawley to gain promotion.
"He was a real personal friend to me. It's been difficult since I got the call," Evans said.
"He is a fantastic man and his work has given us a platform to build success on for years and years.
"What he has put in place is quite extraordinary for a football club.
"There will be a few nights when I shed a tear."
Crawley took a further step towards clinching the Blue Square Bet Premier title with a 2-1 win away to Eastbourne Borough on Tuesday.
What Bruce has put in place is quite extraordinary for a football club
Crawley manager Steve Evans
The Sussex side now lie 12 points clear of AFC Wimbledon, with three games in hand.
"It was fantastic to see his wife Silpa," Evans continued. "She got the kind of ovation that showed what people think of her husband.
"She has got a big role to play with us as a football club."
Source: BBC Sport
Source: BBC Sport