Australia lost the series 2-1 and Smith apologised for letting his "emotions falter" several times during the four-match rubber, which was marred by acrimony between the two sides.
O'Keeffe feels Smith led with sincerity but he is too emotional for the high-pressure job.
"He leads from the front (and) he's finding out about leadership," O'Keeffe said on 'Fox Sports' Back Page Live'.
"Is he temperamentally sound enough to be the captain of our country? Probably not because he's so emotional. We've seen when he's on the field he's overly reacting to everything," added the leg-spinner, who played 24 Tests for Australia and picked 53 wickets.
"That catch was (not) cleanly taken. He decided to go with the cheat line. There's an emotion to Steve Smith that basically is at the core of his game," O'Keeffe said.
Smith, however, had a fantastic series with the bat, making 499 runs.
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