"We are playing a good brand of rugby," said O'Connell, after the Lions outscored the world champions three tries to one in Durban.
"I think we ran out of time. We were playing quite well. When we did what we wanted to do, we were getting over the gain line and we were opening them up a bit. The more we did that, the stronger we grew.
"If a few of our try-scoring chances had stuck, it would have been game over and we would have won it."
O'Connell also lamented the number of penalties his side gave away, especially during a first half in which they trailed 19-7 after 40 minutes.
"When the ref gives that many penalties against you, you don't really stand a chance," O'Connell told Sky Sports.
"It was just penalty after penalty after penalty against us. Undoubtedly some were our fault but it was a killer for us.
"It was a very bad try to concede after two mauls (Heinrich Brussow scored for the Boks after 45 minutes). That hurt us badly, but the scores from the penalties killed us as well.
"If we had cut out the penalties then I think we would have won the game."