The Portuguese side earned a 1-1 draw in Switzerland in the first leg, but they were on a different level to their opponents at Estadio do Dragao, cruising to a crushing triumph in Porto.
Yacine Brahimi caught the eye in particular, scoring the first and then setting up Hector Herrera for a delightful second.
Casemiro added the third with a spectacular long-range free-kick, before Vincent Aboubakar – starting in place of the injured Jackson Martinez – added his name to the scoreboard with a sumptuous 20-yard finish.
The victory secured Porto's place in the last eight for only the second time since the club's victorious 2003-04 campaign and Lopetegui is adamant that they have reached this stage on merit.
He told TV1: "The whole team is to be congratulated for a superb display against a tough and very experienced opponent that came with the clear intention to progress [to the last eight].
"We deserve to be in the quarters. We came into the Champions League without an automatic spot, got a place in the group stage, which is not easy, and now we are with merit among the top eight in Europe.
"It is a great day for all the players, who are happy. As a coach I'm very proud of them."
An injury to right-back Danilo following a first-half collision with goalkeeper Fabiano seemed to put something of a downer on a glorious night for Porto, but Lopetegui revealed that the Brazilian's injury is not serious.
"The team was changed, it was a dramatic situation," the Spaniard added. "He [Danilo] is fine and that's the most important thing.
"The team reacted well. I've always known what I would do. We showed a lot of character, never settled for a result but [sought] only to improve it."
