Stockdale, 43, was in the thick of the action during last Thursday's Individual Final, finishing 16th to round-off a memorable Olympic experience.
Riding John Bosher's Corlato, Stockdale produced a foot perfect clear in the first round to finish in the top 10 going forward to the second.
Speaking after the first round, he said: "I'm absolutely delighted, she's been going well all week and the fences she had down are more than she's had all season."
"I was lucky at the last, but I'll put it down to jockey nerves – it is the Olympics after all!"
The second round, however, bought disappointment to the British camp when Stockdale and Corlato crossed the line with an uncharacteristic 16 penalties to finish in 16th place from 20 finalists.
After it was all over, a slightly disappointed Tim reflected: "Our preparation outside was very good and I thought a clear round might have been on the cards, but once in the arena she was jumping high enough but not wide enough."
He added: "That's the way it goes."
Stockdale had earlier helped a three-man GB team finish in 7th place in the Team Jumping Final.
Reflecting on Stockdale's contribution to Team GB, British Team manager Derek Ricketts said: "Tim gave a solid performance."
"He was unlucky in the last round of the individual final when the heat and humidity appeared to take its toll."
"Tim and Corlato have proved themselves a mainstay to the British Team this year and they will now go on to represent Great Britain at the Samsung Super League Final in Barcelona next month."
Despite his disappointment at finishing outside the medals, the finalé turned out to be one of the most exciting Olympic finals in history.
A double clear from Sweden's Rolf Goran-Bengtsson and Canada's Eric Lamaze meant a jump-off ensued to decide the gold and silver medals.
The Canadian produced yet another clear to take the gold, with Rolf Goran-Bengtsson lowering a single fence, claiming the silver.