Home fans could have been forgiven for expecting their side to run up a huge tally against the Group C minnow, but they had only Mario Gotze's goal to show for their first-half dominance.
"We had many chances but did not score enough goals," he told kicker.de. "That is precisely our problem. We're not good enough with the opportunities we get.
"In some situations we could have done better. We sometimes made small errors and did not find the finish we needed."
While the 2010 semi-finalist could afford such wastefulness against
Ozil added: "We put pressure on from the start and wanted to score an early goal.
"With so many missed chances in the first half we made the game interesting, but we gave everything and deserved to win.
"We can be satisfied with the result, we gave everything. We have taken the first step."
Playmaker Gotze paid tribute to the Faroes' defensive efforts, though, admitting: "They stood very deep and it was difficult to get through.
"We should have been a little more consistent (in front of goal) but we took the goals well."
Olsen also felt his team's efforts should be appreciated and reserved special praise for former Manchester City goalkeeper
"Our goalkeeper had a great day today," he said. "He saved many goals.
"All the players worked very hard to limit the damage. We cannot be unhappy with this result."
FIFA World Cup
A US man trying to dribble a football 16,000 kilometres to Brazil in time for the 2014 FIFA World Cup has died after being hit by a pickup truck on the Oregon Coast.