Barcelona did not threaten early on, and went ahead thanks to an own goal from De Rossi, before Manolas scored another own goal to make it 2-0.
A rebound from Pique made it 3-0, saves from Ter Stegen kept City in the game, before a Suarez strike came after Dzeko’s goal.
Despite the own goals, Valverde believes they deserved to win.
“During the season there are all types of games – ones where you deserve more than you get and ones where you get more than you deserve,” he said.
“We scored the goals we deserved, they attacked us and got the goal they were looking for which made our fourth very important.
“We do not care that they were own goals. If you do not get close to the goal, you do not get own goals. If the opponent scores in their own goal, what are we supposed to do?”