The Blues's boss led her side to a third consecutive WSL title on Sunday, beating Manchester United Women 4-2 on the final day of the season.
The Blues' victory saw them beat London rivals Arsenal to the top spot, on a dramatic last day which saw Eidevall's side win 2-0 against West Ham but the result was in vain.
The Gunners had looked favourites to take the title after a strong start to the campaign, including an opening day victory over WSL dominators, Chelsea.
However Hayes' side soon caught up with their London rivals, winning nine times in a row as the season drew to an end, capitalising on Arsenal's only league loss of the season that came against Birmingham City in January.
In the end, Chelsea were crowned champions with just one point separating them and second placed Arsenal.
And Hayes told talkSPORT she's enjoyed the rivalry between the Londoners - particularly with Gunners boss Eidevall.
"Of course I do I love that part [the rivalry between the managers], there's no point denying that." Hayes told talkSPORT Breakfast.
She continued: "I think any rivalry is healthy, I welcome it, I like the competition, it improves me as a coach and I think Jonas has been an amazing addition to the league this year.
"But I'm absolutely delighted he's sitting at home empty-handed today!"
Celebrations are yet to truly begin for the WSL winners as they look to add to their trophy cabinet on Sunday in the FA Cup final against Manchester City.
However, whilst focus is currently on the FA Cup, it's the push to win the WSL title that Hayes has praised her side for, given how hard they worked to clench it.
"We were chasing the whole season, we knew we didn't get off to a good start and I think that challenge was one my team thrived on." Hayes said.
"For whatever reason, they seemed to perform better in difficult moments, whether it's going down to ten players, whether it's losing to Arsenal first game of the season, whether it's going 2-1 behind.
"And Erin Cuthbert said to me, we played in the first half like we had something to lose, and in the second half we played like we had everything to win."
She continued: "Because we've been used to winning for such a long time, that challenge resonates the most with the group this year, and that's why we've been victorious."