The quartet were always long shots for a medal, despite finishing fourth at last year's World Championships in Daegu, and were never in race won by a powerful USA quartet with Russia and Jamaica completing the podium.
But they won't be happy to be ran out of fourth by the Ukraine, claiming fifth place in a season's best 3:24.76.
“We knew it was going to be hard but we always aim high and aim right for the top," said Ohuruogu, who joined forces with Shana Cox, Lee McConnell and Perri Shakes Drayton.
"In a relay race you never know what’s going to happen.
"We came here at least hoping to put in the best effort we could put in and try and come away with something.
"We knew it was going to be difficult. We came out here to do the best we could and I think that’s what we did. It would have been nice to win a medal, so that's disappointing."
It means Great Britain finishes the athletics events with six medals - four golds, one silver and a bronze.
And despite the memories of Super Saturday - when Jess Ennis, Greg Rutherford and Mo Farah won gold in the space of 44 minutes - and Farah's win in the 5,000m, that could put pressure on UK Athletics head coach Charles van Commenee.
He had targeted eight medals at these Games, including one gold, and had also said he would resign as a 'matter of credibility' if that ambition was not achieved.
But Great Britain's four golds mean they finish fourth on the medal table, their best performance at a Games since 1980, when Allan Wells, Seb Coe, Steve Ovett and Daley Thompson all topped the podium.
Indeed, only the USA, with nine golds, Russia with eight and Jamaica with four but 12 in total had a better return of podium spots.