After the game Hazard apologized to the 17-year-old ball boy, who also said sorry to the Chelsea forward, though the Belgian is likely to be banned for a minimum of three games by the English Football Association for lashing out in the way he did.
The ball boy furor is the last thing under pressure Chelsea interim manager Rafa Benitez needs just now.
Hazard's kick and red card is just the latest in series of setbacks following the club's exit from the European Champions League and its dismal league form which has seen the London team fall 11 points off the lead, leaving Chelsea to focus on cup competitions -- the FA Cup and the Europa League.
The Hazard incident overshadowed Swansea's achievement of reaching a first major cup final in its 100-year history after their 2-0 aggregate win over Chelsea.
The Welsh club, which almost went out of the Football League 10 years ago, will now face fourth-tier Bradford City in the League Cup final at Wembley on Feb. 24.
"Over two legs Chelsea had the ball more than us," said Swansea manager Michael Laudrup.
"That is normal, that is Chelsea, but today they didn't really have any good chances. We had some good chances.
"They had to score at least two but to be honest we deserved it. They didn't score once in 180 minutes.
"What Bradford has done - there are no words. They have beaten three Premier League teams, it is marvelous. If I had a hat on I would take it off."
In the Premier League, Arsenal thrashed West Ham 5-1 at Emirates Stadium.
Olivier Giroud scored twice, while Lukas Podolski, Santi Cazorla and Theo Walcott were also on target for the Gunners.
Arsene Wenger's men are now four points off fourth place which holds the coveted prize of Champions League football.
In Spain, Real Madrid booked its place in the last four of the Copa del Rey, despite being reduced to nine men during the 1-1 draw at Valencia.
Leading 2-0 from the first leg, Real opened the scoring a minute before the break through Karim Benzema.
Alberto Costa's 52nd minute strike brought the home side level before Fabio Coentrao and Angel Di Maria were sent off.
Jose Mourinho's side will play Malaga or league leader Barcelona in the next round.
In the night's other tie, Sevilla cruised past nine-man Real Zaragoza 4-0 thanks to two goals from Alvaro Negredo.
Zaragoza lost defender Jose Fernandez to a straight red card after 26 minutes before Fran Gonzalez followed him down the tunnel 40 minutes later.
Spain striker Negredo fired his side ahead after 36 minutes before Ivan Rakitic doubled Sevilla's advantage.
Negredo netted his second from the spot before Manu del Moral completed the rout to set up a last-four clash with either Atletico Madrid or fierce rival Real Betis.