Fran Kirby and Sam Kerr skewered City as the Lionesses star bagged a brace and Kerr helped herself to a cup final hat-trick at Vicarage Road.
A sickening injury to Maren Mjelde soured the second half but Hayes remained proud of her team's display.
“We were unbelievable for 60 minutes," Hayes said. "The pace, the intensity, the movement, the cohesiveness was brilliant. It was a great team performance.
“It’s only what we’re capable of. You can’t underestimate how hard it is to play at top levels week in, week out. Your performances have different positive aspects to them, this was the performance of a confident team and I really enjoyed the game.
“I did think it would be a tighter affair. But when you score so early, it gave us the belief we needed to go on and we could have scored more than six. That’s not a discredit to Bristol, you have to talk about my team and we were exceptional going forward."
Matt Beard’s side had barely been able to form two banks of four before Chelsea opened the floodgates, Kirby beating her marker on the right and squaring for Kerr to tap home.
The pair combined again for the second on ten minutes when Yana Daniels was caught in possession, Kirby played in Kerr and the Matildas star picked out the far corner.
It was three when goalkeeper Sophie Baggaley’s pass was intercepted and Kirby chipped home on the half-hour.
The 27-year-old, fresh from penning a new contract at Chelsea, is unplayable in this kind of form and made sure of the result on 35 minutes.
Kerr breezed past Bristol skipper Gemma Evans and found Kirby, whose shot was parried by Baggaley but not firmly enough to keep it out.
Beard’s outfit started the second half brightly but were picked off on the counter-attack, Ann-Katrin Berger’s quick kick finding Kirby who slid the ball across to Kerr for the fifth.
Five minutes later, Kirby turned provider again as she slipped Guro Reiten in for a simple finish.
Mjelde's knee injury stymied Chelsea’s momentum, but they remained imperious on route to another major trophy.
Beard's Bristol City emerged bloodies - a flyweight going up against one of club football's heavyweights - and the Vixens boss criticised his side's passivity in the first half.
"The occasion got the better of us," said Beard.
"The frustrating thing is the first three goals came from our mistakes, which was disappointing. But we can take a lot from this experience.
"I was disappointed with how deep we were, how respectful we were. We allowed them too much room and if you give Chelsea too much room, you're going to get punished.
"We showed them some footage at halftime of how deep we were, to show them that the space was there. We looked better in the second half and created a few chances when our shape was higher."
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