"I am not disappointed as they have a very good side", said Carvalhal, who took Swansea to the last eight for the first time since 1964.
Tottenham headed to Swansea yesterday without three of their most talented players in the starting XI.
The ties will take place at Wembley on the weekend of 21-22 April.
United will face a Tottenham side who have enjoyed great success under manager Mauricio Pochettino but are without a trophy since they won the League Cup back in 2008.
"It was important to see a reaction today and we're through to the next round and we're happy".
Son Heung-min, leading the line for Spurs in the absence of the injured Kane, then had a goal ruled out for offside following the intervention of VAR. At the other end Dier's long-range shot was tipped wide by Nordfeldt brilliantly as the game opened up. As Tammy Abraham pounced on the loose ball, a goal looked inevitable, but the striker headed straight at the Spurs goalkeeper from six yards out.
Swansea made a change at the break, replacing Kyle Naughton with Luciano Narsingh, but the pattern remain unchanged as Spurs pressed for a third goal.
It was embarrassingly easy, though not entirely unpredictable considering the fact Swansea had not beaten Spurs in 14 Premier League attempts and have to go back to 1991 for their last win over Tottenham. A cross from the left nearly found Lucas Moura at the near post but he couldn't quite get on the end of it, then Eriksen had a curling effort tipped onto the bar by Nordfeldt and Eric Dier nodded just over as Tottenham totally dominated the first half.