Appeal on cards after Mirallas sees red
Manager Roberto Martinez will examine replays of the Belgium winger's dismissal before deciding whether to lobby the Football Association to get the decision overturned.
Mirallas, a stoppage-time replacement for Ross Barkley, had barely been on the field when he was penalised for a high challenge on fellow substitute Modou Barrow and shown a straight red card.
The 27-year-old is likely to face a three-match suspension, starting with Tuesday's League Cup third round tie at second-tier Reading, if referee Stuart Attwell's decision stands.
"I always tell my subs to come on with real intensity so I was pleased with Kevin's manner," said Martinez.
"I felt he was a striker trying to defend himself and maybe putting in a defensive challenge which looked worse than it actually was.
"I haven't seen it in detail but sometimes you (referees) need to show a little more common sense and I felt that he clearly didn't have the intention to hurt the Swansea player.
"It was more Kevin being fired up, trying to get the tempo of the game and trying to help the team.
"I'm disappointed with the action but not with his manner. I haven't seen it again but we'll look at it and if there's grounds for an appeal we'll look at it."
- Defenders -
The late loss of Mirallas compounded a frustrating day for Martinez, who saw his side dominate the second half at the Liberty Stadium but fail to score following a closely contested opening 45 minutes.
They enjoyed 52 percent of possession and had more attempts on goal than their hosts, with striker Romelu Lukaku failing to capitalise on the best of the opportunities.
Star billing, however, went to Martinez's youthful, all-English defence.
The Spaniard handed a full Premier League debut to 21-year-old right-back Tyias Browning alongside centre-back John Stones, also 21, and 19-year-old left-back Brendan Galloway.
They were marshalled by Phil Jagielka, 33, but it was Stones, a summer transfer target for Chelsea, who really caught the eye.
"I think it was a reflection of our football club and I want it to be that way," said Martinez.
"To keep a clean sheet with that youth, and the amount of decisions those two youngsters had to make made me extremely proud of what we are as a football club.
"Young players will be given opportunities here and they have to be good enough to take them."
Despite dropping two points at home, Swansea manager Garry Monk was pleased with his team's response to last weekend's 1-0 defeat at Watford.
He saw his defenders withstand intense Everton pressure with several members of his back four making important blocks.
Monk said: "It was a very even game. The key to it would have been that first goal. They had chances, we had chances.
"It was a good point and I thought it was a good advert for the Premier League with both teams trying to go for it and score goals.
"Getting a clean sheet is pleasing. Everton have got some great players. We showed we are at least on an even keel with them.
"I'm much happier this week than I was last week against Watford. If you can't win a game you don't lose it so it was night and day compared to last week."