Villarreal, third in the Spanish Primera Liga, have seven points from three matches in Group E, which also includes Manchester United.
Llorente said that despite the convincing result, it was a difficult match for Villarreal.
"We were suffering a lot, it was a tricky match against a team that appeared inferior but which showed that they can do something if you let them," said the 28-year-old, who was bought from Valladolid last season. "It was not a good first half, but in the end it came out alright."
The Danish side's Polish forward Marek Saganowski, on loan from Southampton, who opened the scoring in the 19th minute with a diving header from a cross by Anders Due.
Guiseppe Rossi leveled it nine minutes later after Angel Lopez advanced into the penalty area and cut the ball back for the USA-born Italian.
Joan Capdevila put the Spaniards ahead for the first time in the 33rd minute when he picked up an aerial clearance by the Aalborg defence, controlled the ball with his left foot and delivered a perfectly placed lob into the top corner of the net, leaving Moroccan keeper Karim Zaza with no chance.
Saganowski then split the Spanish defence with a shot deflected to Thomas Enevoldsen who rounded Diego Lopez in the 36th minute to make it 2-2 at half time.
In the second half, Llorente came on for Guille Franco, and proved an inspiration. In the 67th minute, he seized on a shot that Zaza could only parry from Marcus Senna to score the first of his three goals.
Swedish international midfielder Andreas Johansson gave the Danes some hope with a headed goal in the 77th minute, to reduce the deficit to 4-3.
Another substitute, French winger Robert Pires, who came on for Mati Fernandez, picked up another for Villarreal.