Taking charge of his maiden La Liga match as Madrid head coach after replacing Zinedine Zidane, Lopetegui oversaw Madrid's 2-0 win over Getafe at the Santiago Bernabeu on Sunday, FourFourTwo reported.
Madrid suffered a 4-2 extra-time defeat to rival Atletico Madrid in the UEFA Super Cup last time out but Lopetegui's men bounced back thanks to Bale and Dani Carvajal.
After Carvajal opened the scoring in the 20th minute, Bale – headlining Madrid's forward line following Cristiano Ronaldo's move to Juventus – doubled the lead six minutes into the second half.
Discussing Bale's performance afterward, Lopetegui told reporters, "I liked the team's performance in general and Bale had a very good match.
"He offers lots of different things, like the other players. We must continue working, the team always comes before individual talent and that goes for Bale too."
Lopetegui added, "We're satisfied with the win and happy because the team did a lot right. There's still room for improvement at this stage of the season, as with all teams. We played with intensity, played as a team and scored two goals against a side who had the third best defensive record last season and who came here and made things difficult.
"We're happy that we didn't give them many chances and that we created a lot. We want the team to attack and defend well. Not conceding is fundamental and it's a basic in order to compete. Today we got things underway in La Liga and we have to keep improving because in a week we've got a demanding match in Girona, which forces us to keep improving."
There was no debut for Thibaut Courtois in the Spanish capital as Keylor Navas retained his place against Getafe.
A high-profile arrival from Chelsea, Belgium international Courtois sat out the Super Cup clash and he had to settle for a place on the bench for Sunday's league opener.
"We'll be running with three goalkeepers in the squad. We're delighted with the competition for the goalkeeper's jersey. It's marvelous and I don't see it as a problem, but rather see it as us having several options," Lopetegui said.
"We'll make decisions as the season progresses. We're really happy with the performance levels of our goalkeepers."
Gareth Bale said he is feeling good after scoring in Sunday’s game.
Speaking after the match, Bale said, "I'm feeling good and, although I scored, the most important thing was that we got the win and are continuing to improve as a team.
"We're really looking forward to the season ahead. Our target, just like every year, is to win all of the competitions we're involved in and we'll be giving our all to do just that.
"The new signings have adjusted really quickly. We've given them a good welcome and I hope that they're all available in the near future."