Following on from Sunday's hat-trick against Manchester United, Haaland scored City's first two of the night before an own goal from David Khocholava and second-half strikes from Riyad Mahrez and Julian Alvarez.
Such was City's dominance that Guardiola could withdraw Haaland at half-time after seeing him score his 18th and 19th goals of the season for City.
The day had started with reports in Spain that a clause in the 22-year-old's contract would give Real Madrid a free run at signing him as soon as 2024, but Guardiola said there was no truth to the report.
"It's not true," the City boss said. "He has not got a release clause for Real Madrid or any other team.
"The rumours and people talking, we cannot control it. I always worry about what we can control.
"What's important is he has adapted really well, we have the feeling he is happy here. We will try with him and all of them who want to stay to make them happy.
"In the future, nobody knows, but he is happy, he has settled perfectly, he is incredibly loved and this is the most important thing."
Guardiola said the decision to replace Haaland with Cole Palmer at the break was not pre-planned, but with City already in cruise control with a 3-0 lead five minutes before the break, he took the opportunity to give him a breather ahead of Saturday's Premier League match against Southampton.
"He has played a lot of minutes," Guardiola said. "Of course Cole Palmer is an excellent player, I'm looking forward to him playing.
"If the game was tight Erling will continue to play but after that it is better to rest and think about Southampton, a team we were not able to beat last season."
There were suggestions the decision might have signalled an injury for Haaland, but after returning to the bench late in the second half, the Norwegian ran on to the pitch to celebrate with his team-mates after the final whistle before jogging around applauding supporters.
Haaland might have been disappointed not to be allowed the opportunity to seek yet another hat-trick, but if he was, it did not show.
"Erling wants the same as all of us - to win the game," Guardiola said. "He made the hat-tricks to win those games. Of course if he had played another 45 minutes he would have had more opportunities but we need everybody involved."
Guardiola had made five changes from Sunday's derby victory. Aymeric Laporte made his first start of the season after injury, linking up with the returning Ruben Dias in defence while Alvarez, Mahrez and Sergio Gomez also came in.
"It is not about resting players," Guardiola said. "It's about a squad of 20 players, not just 11. This was the best selection to win the game because we need the players everywhere in this tight, tight schedule.
"It was an excellent result and a better performance. People say, 'It's Copenhagen' but they defended really well, but we play the movements with the ball and without the ball.
"Today we see the reason for success for this club. After Man United, 6-3, there were a lot of compliments but we are humble enough to respect the opponent Copenhagen. This is the secret of this team. The work ethic in training, everybody is focused, everybody pays attention.
"This is why this season and in previous seasons, with important players, we are there every three days. This is the biggest title we can get. Beyond the Premier League, Champions League, everything. This is the best."