United got off to the perfect start as Romelu Lukaku rifled a shot into the top left-hand corner after just five minutes. The Red Devils dominated the first half and doubled their lead through Alexis Sánchez's low drive which found the bottom corner after being played through by the impressive Jesse Lingard.
The Swans were much-improved in the second half and would have got themselves back into the game had David De Gea not kept out Tammy Abraham twice in quick succession with two superb saves.
However, in the end United were able to comfortably hold out to claim the three points and enhance their grip on second place in the Premier League, much to the delight of Mourinho.
"The first half was perfect, with one more goal it would have been game over. In the first half they did not cross the half-way line or have a shot. We had lots of movement and passing."
He added: "We got into lots of dangerous positions and scored twice but should have had at least one more.
"The second half was different. Credit to Carlos (Carvalhal) because he changed the team at half-time. I could feel the intensity went down in the second half."
Best performance from Sánchez in a United shirt?
There is no doubt that it has taken Sánchez time to settle into life at Old Trafford following his January move from Arsenal. However, his performance against the Swans, especially in the first half, summed up why he can be one of the most dangerous players in the division when he is at the top of his game.
Despite this, Mourinho was keen to reflect on his side's performance as a collective rather than focusing on individual players. He said: "The team played very well. I do not like to make it about individual performances. Alexis played well but I think everybody played well in the first half.
"In the second half, I think Alexis was one of the players to pay the price of playing international football."
Mourinho was not particularly happy with his side's performance in the second half as they lacked the same intensity they had shown in the first. However, the 55-year-old manager believes this has a lot to do with the fact that majority of his side had been involved in international friendlies.
He said: "We let them (Swansea) have the ball and did not press so high. Some players who were amazing in the first half went down a little bit.
"They felt that they had a chance and David (De Gea) made a couple of good saves. With seven matches to go, it is all about the points. We are going to fight to stay in second position."
Looking ahead to the Manchester derby
United's next match will be against bitter rivals Manchester City next weekend at the Etihad Stadium. If the Citizens win, they will be crowned Premier League champions. However, Mourinho played down the importance of the fixture and was instead keen to focus on what he believes has been a very positive season for his side.
He said: "I am not thinking about it yet. Instead of being critical about our second half, give Carlos credit for changing two players. Not many coaches would change two players at half-time.
"Manchester City is not important for me. We have been in second for majority of the season and deserve to be in second. Despite of what you say, you say the fourth, the fifth, the sixth are all better than us but they are not better than us.
"We have more points than them. We are going to fight in every match to finish second."
Mourinho heaps praise onto Carvalhal
In an upbeat mood following his side's victory, Mourinho invited Carvalhal to join him in his press conference as he finished taking questions from the press.
On the impact his fellow countryman has had at Swansea since arriving, Mourinho said: "This guy is going to keep Swansea in the Premier League and is manager of the season."
He added: "In the second half, his team improved. The international week made a few of the boys go down in their intensity. We gave them more space to play."
Mourinho's post-match press conference ended with him being questioned on the impact of 24-year-old striker Lukaku, who scored his 100th Premier League goal against the Swans with an emphatic finish.
He said: "It is not just about the goals. It is about the work he does for the team. He is a very humble guy and a great player. Even his defensive movement, he is really good."
If United can perform in a similar fashion to how they did in the first half over the full course of the match at the Etihad, they may have a chance of delaying City's celebrations for a while yet.