Barcola completed a high-profile move to Liverpool for an initial 125 million euros, with a further 20 million euros potentially due in bonuses. The 24-year-old had two years remaining on his PSG contract but had decided he wanted a bigger role.
"Everyone is a winner," Luis Enrique said ahead of PSG's Ligue 1 meeting with Monaco on Friday.
"He wanted to leave because he wanted to have more importance in the team. And that is something that you have to earn in training. I can't guarantee that to any player."
Barcola was an important member of the PSG squad last season, scoring 13 goals in 49 appearances in all competitions as the club retained their Ligue 1 title and won the Champions League.
However, his position in Luis Enrique's starting XI was not guaranteed, with Khvicha Kvaratskhelia also competing for a place on the wing.
"He has been a very important player for us, and he is an incredible person," Luis Enrique said. "He was liked by his teammates. He still had two years left on his contract, but he decided to leave, and I wish him all the best. We have to accept it."
PSG have moved quickly to strengthen their attack following Barcola's departure. Ferran Torres arrived from Barcelona, while Maghnes Akliouche joined from Monaco and Mika Godts was signed from Ajax.
The three attacking additions have cost the club around 150 million euros combined.
"I am happy with the three players we have brought in up front," Luis Enrique said. "We must not make comparisons. We will see what happens, but I am happy with the transfer window."
The Spaniard knows his new forwards will need time to settle, particularly with PSG still searching for their first Ligue 1 win after opening the campaign with draws against Rennes and Lille.
PSG also suffered defeat to Lens in the French Champions Trophy after previously beating Aston Villa in the UEFA Super Cup.
Despite the uneven start domestically, Luis Enrique remains focused on PSG's biggest target when their Champions League defence begins against Slovan Bratislava next Wednesday.
"Our objectives are clear," he said. "I have said it many times. I want to win the most important trophies, and there is none bigger than the Champions League."
Gabriel Martinelli has admitted his decision to leave Arsenal for Saudi Pro League giants Al Hilal was not entirely in his hands after ending a seven-year spell with the Premier League champions.
Leeds United manager Daniel Farke has confirmed that Joe Rodon could be out for up to 10 weeks after suffering a hamstring injury.
Liverpool manager Andoni Iraola has backed new signing Bradley Barcola to make an immediate impact as the Reds prepare to face Ipswich Town on Friday.
Jose Mourinho faces an early selection headache at Real Madrid after Arda Guler, Eduardo Camavinga and Bernardo Silva were ruled out of the Champions League clash with Inter Milan.
