For the second year running, Arsenal bested their London rivals in the Conti Cup showpiece at Molineux, where an extra-time Stina Blackstenius strike saw Eidevall's side defend their crown.
However, Hayes had evidently taken issue with Eidevall's actions during the final, as the Chelsea boss was seen giving the 41-year-old a slight shove as they shook hands at the full-time whistle.
Hayes also wagged her finger to a perplexed Eidevall, who had a few more words to say to his opposite number before Arsenal staff intervened, and the Chelsea boss explained her anger towards the Arsenal coach at the full-time whistle.
Eidevall and Chelsea's Erin Cuthbert engaged in a brief war of words over a throw-in, which Hayes slammed as 'unacceptable male aggression' and claimed that the Swede should have been sent off.
Eidevall: 'Others need to look in the mirror'
"I'm not down for male aggression on the touchline, I'm really not. And fronting up to players, for me, that's unacceptable. I'm disappointed and I told Jonas that. I don't think it's OK to behave like that," Hayes told reporters.
"He got a yellow card, and he should have probably been sent off. I'm all for competing to win, I've never been booked in 12 years, my time here, I totally accept he's a winner and wants to win but his behaviour on the touchline wasn't acceptable."
During his own post-game press conference, Eidevall opened up on his touchline set-to with Cuthbert, referencing Chelsea's desire to use just one ball in the final but then wanting to use a different ball in order to take a quick throw.
"I think that's a very irresponsible way of labelling the behaviour that I have, I don't feel comfortable with that label, I don't think it's the truth to do that, so I think it's very irresponsible to do that," the Evening Standard quotes Eidevall as saying.
"The ball gets kicked away and Chelsea want to take a new ball to throw a quick throw-in and I said, 'You guys wanted to play with one ball, now we need to get that ball'. Of course, Erin doesn't get happy over that, I didn't say anything more in that situation.
"If we decide to play with one ball we play with one ball. I like to play with multi-ball, the game is quick, but they didn't want to do it and you can't do it when it suits you.
"I think there is definitely a way you behave in the technical area, there is also a way you behave after the game, being a good winner, but you also need to be a good loser and be responsible in both those situations. I'm happy with the way I conduct myself and others need to look in the mirror and see if they're happy with themselves."
Frida Maanum "stable" after distressing collapse
Amid Eidevall and Hayes's fracas and Arsenal's celebrations, Sunday's final was overshadowed by a distressing incident involving Gunners midfielder Frida Maanum, who collapsed on the field in extra time and received oxygen as she was taken off on a stretcher.
The Gunners confirmed that the Norwegian midfielder was in a stable condition, though, and she was reportedly able to travel home with her teammates without the need for a hospital assessment.
Following the international break, the Gunners return to Women's Super League action on April 14 at home to Bristol City, and they sit nine points behind leaders Manchester City in third place with a game in hand.