"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.
In Italy, AS Roma claimed a 2-1 win over Inter Milan in the first leg of its Coppa Italia semifinal.
Alessandro Florenzi headed home Ivan Peris' cross on 13 minutes with Mattia Destro adding a second.
Inter pulled goal back just before the break when Rodrido Palacio latched on to Esteban Cambiasso's free-kick and fired into the net.