The Swans boss had talked prior to kickoff about the North Londoners being favourites in the contest and was proud of his side's performance afterwards.
"It was a tough game," Carvalhal told BBC Sport at full time.
"First I want to say two quick things: We achieved the best run in the FA Cup since 1964, this cup this season we put all the squad to play, we give importance to it but our main competition is trying to save the team. So after this, we move to the Premier.
"We played against a strong side - I said before the game it was David against Goliath, we know the difference between the teams. For us to progress, we would have to be at our best, and they have a bad afternoon. They took the game very seriously, the way they played, they deserved to win.
"We have to prepare for our next game, we have days to rest a little and breathe a little, some players will go to their national teams but we believe we will be back at our level again in the Premier games."
Swansea continue their fight for safety in the Premier League with a trip to Old Trafford to face Manchester United on March 31.