The Blues lost 2-1 to Manchester City in the final fixture of the Women's Super League when a victory would have guaranteed them title glory.
Instead they finished second to Liverpool, but came back this year to win their first-ever piece of major silverware as PFA Women's Player of the Year Ji So-yun scored the only goal to beat Notts County in the first final held at Wembley.
And Hayes reckons the bitter blow of last year played its part as her players wanted to bounce back and show what they are made of.
"Sometimes you have to go through the pain of losing and losing in such extreme circumstances to get to this point," she told BBC's Sunday Breakfast.
"I don't know if we would have gone on if we had won the league last season and been in the same position
But what there has been with my players all season is a drive and a hunger, most importantly they won't let it go.
"We may have had a blip in our league campaign in recent games but I think that was because the FA Cup was on their mind, and understandably so
It is not every day you play at Wembley
It is about winning trophies."
Ji's goal came six minutes before half-time in front of 30,710 fans inside Wembley, an experience Hayes believes no-one at the club will forget.
"There was no way we were going to lose yesterday," she said.
"The team have been preparing for some time and when I watched them work out there was an intensity, a focus to them
They were very strong.
"Playing in front of 30,000 is something everyone is going to enjoy and I can honestly say I enjoyed every single moment of it
It just all came together."
Chelsea sit third in the current Women's Super League standings having lost to both Sunderland and Manchester City in the run-in to Saturday's final.
But Hayes feels the fresh belief instilled in her squad after the FA Cup success can help them push on to take their maiden league crown.
"After this we can kick on," she said.
"We have Fran Kirby coming back into the team and we go into the next game as FA Cup winners and you need that confidence
You need that trophy, it helps you kick on for other honours.
"What success does is breed success and all of my girls will be determined to get another one
It is addictive, you want more of it.
"If we are going to chase more honours we are going to have to put the same level of work in, maybe even more
But why not? We will be determined to kick on and go for the league."
Chelsea have seven games to achieve their ambitions, with their next game coming against struggling Birmingham next Sunday.
Source : PA
Source: PA