Messi, 34, signed a two-year deal with an option for a third year with Mauricio Pochettino's side on Tuesday, and Koeman said it had been a difficult journey for all involved, as the Argentina superstar moved on from the club he joined as a 13-year-old in 2003.
"We have to understand that there is always an end for a player. You have to close the book because now we have to focus on this new season," Koeman told ESPN's Martin Ainstein. "We have new players in and we have to move forward, and we have time for that. We have young players in the squad this season, and it's also for the future, we are working on the future of this club, and it's really important to have our focus on this and not focus on what happened in the last few days."
Messi looked set to re-sign with Barca in recent weeks, but due to a dire financial situation at the club and restrictions imposed on each LaLiga team by the league, he ultimately left to join former teammate Neymar at PSG.
"I knew there was a difficult situation between the club and Leo Messi and the league to have the possibilities to keep Messi in the club," Koeman added. "It takes a long time, but I was also surprised by the day and the moment that I heard that he was finished playing for Barcelona. And I knew the financial situation of the club made it more difficult.
"I think it was difficult because we are not just talking about any player, we are talking about Leo Messi, the best player in the world through a lot of seasons and we were all disappointed that he will not play for us this season. But OK, you have to change fast because you don't stay in the disappointment with the new season starting. You have to understand it was for a few days a difficult situation.
"Messi meant so much for this club."
Koeman sounded optimistic about the start of the post-Messi era as he looked to continue to develop young players and anticipated the return of injured players from last season like Ansu Fati and Philippe Coutinho, while underscoring that Barcelona still have a strong squad.
"Of course we will have more difficulties to score goals," Koeman said. "Messi scored 30 goals last season. So other players need to bring more and take the next step and it's more about the team now than individual players.
"It's not always one player, you have to do it together. Hopefully, we get players back from injury like Ansu Fati and Coutinho and then we still have a strong squad. We will work harder, we will do more to achieve what people expect from us.
"We are still in the transition. We have to understand that the start of this season is difficult. We still have COVID, for all the clubs, but still we have players with injuries so we cannot put all the players for playing because we are still missing good players. We did a good preseason, we have young players in, but if we get all the players back from injury the squad is still a strong one."
Barcelona finished third in LaLiga last season behind Real Madrid and champions Atletico Madrid and bowed out of the Champions League in the round of 16 to Messi's new team, PSG. The Blaugrana did manage to win the Copa del Rey, and Koeman added that the goal of a club like Barca -- to win titles -- had not changed.
"The goal are always winning trophies, being champions, to have a good run in the Champions League," Koeman said. "Clubs like Barcelona don't have seasons out of winning something. We know that, and the football people will understand it will be more difficult. It's all about working rate and the team and we can make a step forward."
Koeman's team begin LaLiga play at home against Real Sociedad on Sunday (stream live on ABC/ESPN+ at 2 p.m. ET in the U.S.).