The visitors were plagued by absences and spent the last 10 minutes playing with a man fewer than the Catalans, but it took a late goal from the Frenchman to get Koeman's side over the line.
"We lacked a lot in the first half," Koeman said afterwards.
"We didn't press them very well. I saw a slow, tired Barcelona from the start.
"We didn't control the game. So we changed the system and improved in the second half.
"It was a difficult game and we were some way off our level. Real Valladolid did a good job defensively, but you have to know how to suffer and I think we deserved to win."