On an emotionally charged day where Wolves paid their tributes to former hero Diogo Jota before the game - they had to soak spells of early pressure and went on to have chances in the first half.
However, they were punished for two errors in the space of three minutes that all but took the game away from them.
Erling Haaland tapped in the opener on 34 minutes while unmarked at the back post - before City capitalised on a stray pass in the middle of the pitch to break with Tijini Rijnders firing past Jose Sa.
Other opportunities then came and went for Wolves early in the second half - as they committed men forward to try and get back in the game.
And as they did that City picked them off, as Haaland bagged a second before Rayan Cherki added a fourth.
Pereira insisted the four goals did not reflect the score line - but they were not able to take advantage of mistakes like the visitors were.
Asked if 4-0 was a harsh reflection, he said: "Of course, but I didn't lose my smile.
"I explain why, because you know for me, my team must be a team with organisation, tactical organisation.
"To be brave, a brave team to try and play our football, to create chances to score.
"We had three or four chances to score goals, but the difference is technically, they are strong individually and technically they are strong.
"Each mistake we committed they punish with a goal.
"In the moments they committed mistakes, we had our chance but we didn't score.
Pereira applauds the fans at full time (Photo by Alex Pantling/Getty Images)
"If you don't watch the game, you would think they create a lot of chances and deserve ten goals and we deserved nothing. No, that was not the case in my opinion.
"Of course I will take good things from this game and the lessons that we need to learn to improve to keep going with our work.
"And of course we need more options to be strong with more options to improve our squad."
Pereira has already made clear he wants more signings to come through the Molineux door before the transfer window slams shut at the end of the month.
Jhon Arias and Fer Lopez were handed debuts from the bench - while David Moller Wolfe was given a full debut at left wing back.
Asked whether he expects new signings before the game, he said: "Before the next game, it will be difficult.
"My expectation is that they, the club, can bring three or four players with quality until the end of the market.
"They know what we need because this league is tough, very tough and we need more quality to add."
The game also saw emotional tributes to former favourite Jota - with Wolves fans paying their respects following his tragic death alongside brother Andre Silva earlier this summer.
Chants throughout the game were coupled with huge banners adorning the South Bank before the game, and Pereira added: "He is still with us, we try to do our best to honour the player, the person, the family.
"But we'll keep him in our heart for the future, he will be with us forever."