The LaLiga giant was left stunned last month when Messi departed for Paris Saint-Germain on a free transfer after it was unable to fulfil a new contract that had been agreed.
Messi's exit has left a big void at Camp Nou, the six-time Ballon d'Or winner having scored 672 goals and assisted 265 across his 778 appearances for Barcelona.
Barca has started the post-Messi era with two wins and a draw in their opening three league matches, scoring seven goals in the process, and Koeman believes his side is adjusting to life without its greatest ever player.
"It was a huge blow to lose him," Koeman said. "We had planned for the season with him.
"We lose so much and it took a few days to get things in order, but we must turn the page and build the team.
"Losing Messi doesn't oblige us to play different tactically but there are things without the ball where the team can improve.
"We won't have the individual quality of Leo, but in pressing and structuring the team, the team is better now."
Antoine Griezmann is another high-profile forward to have left Catalonia last month, the France international returning to Atletico Madrid on an initial loan just two years after swapping clubs.
Koeman understands the club's decision to let Griezmann depart in the final stages of the window, with Luuk de Jong arriving from Sevilla as a replacement.
"The aggravation we had on the last day, with practically no time to find a solution, it was a b****," Koeman said.
"Griezmann had a great contract and if he left it was going to help improve the financial situation of the club. That's why I agreed to his departure."
Koeman has repeatedly called on his other attacking players to step up and new recruit Memphis Depay has done exactly that with two goals and an assist in his first three competitive games for Barca.
Depay also scored his first international hat-trick for the Netherlands in Wednesday's (AEST) 6-1 win over Turkey to move level with Johan Cruyff and Abe Lenstra in Oranje's list of all-time top scorers.
President Joan Laporta revealed this week Depay's number nine shirt is now the biggest seller at Barca and Koeman has backed his compatriot to be the face of the club for years to come.
"Memphis can mark an era at Barca," Koeman said. "He has something that is essential to be a success here: personality and character.
"There's something different about him and he's really motivated by the challenge of being here."
He said: "There are always things to improve but I'll tell you one thing: if we have everyone available, we can do big things.
"We have a great team. We still have to be realistic, it will be difficult, but I am optimistic and ambitious."