The former Rangers defender, who came on as a substitute during the 2-1 extra-time defeat, said that his side came close to doing something "extraordinary" in Brazil.
"We were very, very close to doing the extraordinary," he told reporters. "We remained level with this great Germany for 90 minutes. We showed great quality and strengths. I'm very proud of what we've done.
"I think the goal in the first half could have made us more confident - there were a lot of chances - but it didn't happen. We reacted well to both goals. When a team plays with such heart, it's the foundation you need to succeed."
Germany will take on France in the quarter-finals following their victory over Algeria.