The Blaugrana beat Gimnastic 3-1 in a friendly match at Estadi Johan Cruyff on Saturday, their first outing since Koeman took over from Quique Setien.
With Lionel Messi captaining the team for the first time since announcing he will stay at the club, Barca scored through Ousmane Dembele and a penalty each from Antoine Griezmann and Philippe Coutinho, with Javier Bonilla getting a goal for the Segunda B side.
Koeman changed all 11 players at half-time but stuck with a 4-2-3-1 set-up, a system he appears likely to keep for the start of the LaLiga season.
Explaining that decision, the former Netherlands boss told Barca TV: "The midfield system is a little different to previous seasons but the team has the quality to do that and do it well.
"We're looking to move the ball much quicker high up the pitch to break the lines [of the opposition], to create space and generate more dangerous [situations] so the team scores goals.
"It was our first match in pre-season and that is why everyone only played 45 minutes. They need to build rhythm and play with intensity. It was a little better in the second half than the first. Not picking up any injuries was also very important as we looked to set the tempo in the match. That was more important than the final result.
"All the boys did well and we saw some who hadn't played before. There are always things which can be improved upon but, in general, we are very happy with how the players did after just two weeks of training.
"It isn't a normal six-week pre-season. We've only got four weeks and some even less because they've gone away with their national teams or been injured.
"It's important to integrate everyone. It's complicated because all we want is to build up fitness and over the next two weeks add a more tactical side ahead of a complicated league season."
Barca's next friendly match is against Girona on Wednesday.