What a night.
Chelsea booked their place in the semi-finals in the most thrilling way, coming out on top in a penalty shootout after Maren Mjelde also scored from the spot in the eighth minute of added time in extra time.
"I'm just relieved it's over and we're through that," said Hayes. "It was drama, full of drama. I am exhausted. Relieved and exhausted."
Those watching at Stamford Bridge were treated to a spectacular showdown between two of Europe's heavyweights and Chelsea ultimately accomplished a giant-killing.
Lyon, last year's champions and the record eight-time winners of the competition, came to London needing to overturn a 1-0 deficit and almost did when they led 2-1 on aggregate with seconds remaining.
But Mjelde showed composure to keep her side in it and then goalkeeper Ann-Katrin Berger made two stunning saves in a shootout that Hayes could not stand to watch.
"We've never won a penalty shootout as a team so can you imagine what was going on in my mind," she said of the extra-time period.
"I had to be conscious that the penalty takers were [still] on the pitch as I didn't see a goal in us to be honest.
"When I saw Lyon's substitutes coming off the bench - one after another, all world-class talents - I felt we dealt with it well. It was the most character-building performance, even if it was the ugliest."
'Can't believe what I witnessed'
Chelsea played their second match of the season at Stamford BridgeHayes said Lyon would come for Chelsea after their defeat in the first leg in France but felt "momentum would turn" the more likely a penalty shootout decider became.
The Blues, already without injured England defender Millie Bright, lost Eve Perisset and Melanie Leupolz to injuries during the game, while tiredness also started to show among those left on the pitch.
"Our depth wasn't big and players had to come in and play multiple roles," said Hayes. "For Maren [Mjelde] to do what she did with the last kick of the game... she's a Chelsea legend."
Former Leeds striker Lucy Ward told DAZN: "I can't believe what we have just witnessed. It was tight the whole way through.
"It was an incredible effort from everyone involved. Chelsea have had their injuries, the players were out on their feet by the end of extra time.
"The momentum ebbed and flowed throughout the two-legged tie. A fantastic effort from Chelsea."
Berger's 'moment' as history created at Stamford Bridge
Chelsea goalkeeper Ann-Katrin Berger saved two penalties during the shootoutMjelde produced the heroics from the penalty spot - scoring both in extra time and in the shootout - but Berger had the final say.
Her two stunning saves to deny Wendie Renard and Lindsey Horan sparked an outpouring of celebration at Stamford Bridge - Berger sliding towards the corner flag in front of a standing ovation.
The 32-year-old revealed in August that, after four years of being cancer-free, her illness had returned and she was forced to undergo further treatment, making her achievements on Europe's biggest stage even more remarkable.
"She's someone who really thrives in big moments and has done that her entire career," said Hayes.
"She's probably the best penalty-saving goalkeeper I've ever worked with so I felt really confident going into the shootout.
"I felt like this was her moment given everything she's been through."
Berger added: "The girls know that I love penalty shootouts. I feel no pressure. They have to score, not me!"
Meanwhile Mjelde, who came on as a 73rd-minute substitute, said she "had no feelings" when she stepped up to take the crucial penalty in the final seconds of extra time.
"We fought to the end. A crazy game to come back like we did. We never give up," she added.
"There was a delay so [I had to] focus, I had no feelings, just get rid of all, the feelings in my body. Take my time, just focus.
"It's a moment we will never forget. We made history together at home, at Stamford Bridge, in front of our fans. Perfect, it's what we dreamed of."
Chelsea, who remain in the Women's Super League title race and also have an FA Cup semi-final to come, know they will need to recreate these special moments to progress to the Champions League final.
Barcelona - the Spanish giants who beat Chelsea in the 2021 final - stand in their way in the last four as Hayes chases the one trophy that has eluded her in her managerial career.