Safet Susic's men completed their maiden World Cup campaign with a 3-1 win over Iran in Salvador, finishing third in Group F.
A loss to Nigeria had ended Bosnia's chances of reaching the last 16, but only after Dzeko had a goal incorrectly ruled out for offside.
"Despite the victory, we go home sad as we could've gone further," he said.
"The goal they cancelled out against Nigeria I will remember until the end of my life."
Pjanic was disappointed his team were unable to progress further and he also lamented his side's performance against Nigeria.
"I'm glad I scored at the World Cup, but I am sorry that we did not achieve what we wanted," he said.
"If we had a bit more luck we could have got out of the group. We gave our best and it was a great experience for us. In the second game we did not work hard, but we have to look forward."
