Barcelona went into Sunday's fixture with Levante having gone unbeaten for 36 games in Spain's top flight this season, but the Catalan giants suffered a 5-4 defeat.
Coutinho scored a hat-trick during the setback, but the Brazilian playmaker has acknowledged that the team are "feeling so bad" after missing out with just one match to be played.
The 25-year-old is quoted by Marca as saying: "We're not feeling good, we wanted to finish the La Liga season without losing. We played a very challenging match against a team that was very motivated. They scored five past us and deserved to win.
"It was such a difficult night. It was a historic streak for us, 43 games without losing. We feel so bad not to get the record, but our preliminary goal was to become champions."
Barcelona end the season with a meeting with Real Sociedad at Camp Nou.