Second-half goals from Jordan Ayew and Nathan Dyer secured a 2-0 win over Sheffield Wednesday in their FA Cup fifth-round replay at the Liberty Stadium.
Swansea last graced the quarter-final of the competition 54 years ago, and Carvalhal pointed inside his jacket for inspiration ahead of a last-eight meeting against either Tottenham or Rochdale.
Asked if he would allow his players to dream of cup glory, Swansea boss Carvalhal replied: ‘I have ‘Carlos had a dream’ written here in my jacket.
‘All of us have dreams – the people who don’t have dreams are not happy people I think.
‘The main competition for us is the Premier League, but we will have a week to prepare for the quarter-final, which is important, and we are near (to the end of the competition) now.
‘We have 90 minutes to try to get Wembley (for the semi-final) so let’s see what happens.’
Swansea’s last FA Cup quarter-final came in 1964 when Bill Shankly’s Liverpool were beaten 2-1 at Anfield.
The Swans eventually lost a Villa Park semi-final to Preston, ending their hopes of playing in a first FA Cup final.
But those ambitions have been revived and this win was Swansea’s sixth in succession on home soil in all competitions – their best run at the Liberty Stadium since 2007.
‘I am very happy and very proud of my players,’ Carvalhal said after the win over his former club.
‘I was born in 1965. The club didn’t do better than this in the cup since 1964, so it’s been a long, long time.
‘I am happy we have achieved this. Now we will play either Rochdale or Tottenham at home and we could go to Wembley, so we are in a very good position.’
Swansea struggled to break Wednesday down during a turgid first half played in freezing sub-zero conditions.
‘Sheffield Wednesday created problems for us in the first game and also again,’ Carvalhal said.
‘But I thought we had more opportunities in this game.
‘We needed a bit more intensity and a bit more speed in the second half, and that’s why we put Jordan and Martin Olsson on at half-time.
‘We felt after a couple of minutes that we could score and we did that.’
Jacob Butterfield and Lucas Joao both tested stand-in Swansea goalkeeper Kristoffer Nordfeldt in the first half.
And Owls manager Jos Luhakay felt his Sky Bet Championship side were punished for failing to convert early opportunities.
‘The first half was in the balance,’ Luhakay said.
‘We had two or three good chances to score but we did not do so.
‘In the second half we did not make the pressure we like to do, Swansea got the goal and we could not come back in the game.’
Newcastle have been linked with a shock move for former Sunderland goalkeeper Simon Mignolet during the summer.