Sergio Aguero scored a hat-trick, after missing two penalties, with David Silva and Nolito also scoring.
City host the Romanian champions next Wednesday at Etihad Stadium in the second leg of the tie.
"We are very pleased about the way we played. The quality of our players is fantastic," Guardiola said.
The Spaniard, who replaced Manuel Pellegrini in the summer, has won two Champions League titles with Barcelona, but did not lift the trophy in three years with Bayern Munich.
City, who have never won the tournament, entered at the final qualifying phase this season after finishing fourth in the Premier League last term.
"I thank Manchester City for giving me the opportunity to train these amazing players," Guardiola said.
"I enjoy every day in Manchester. I am confident we can make a step forward to make people proud of us."
Aguero has now missed four of his past five penalties for City in European competition, but Guardiola is not planning to take him off spot-kicks.
"I am confident if he's confident," he said. "It's not important how many times you fall down, it's how many times you stand up and try again."
England winger Raheem Sterling, 21, has impressed so far under Guardiola after a difficult first season at City.
He won a penalty - which Aguero converted - in the opening-day 2-1 win against Sunderland. In Bucharest, he was fouled for the first penalty Aguero missed and set up goals for Silva and the Argentine.
"Now he is playing really good," Guardiola told BT Sport. "But he's young and has to learn a lot.
"He has a lot of quality, he's fast, has a good work ethic, can play right or left, go out to the line or go in the middle.
"That's why Manchester City were so clever to buy him last season."
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Manchester City boss Pep Guardiola says his side are "almost in the Champions League" after a 5-0 win over Steaua Bucharest in the play-off round.