When both teams were locked on two goals apiece, the Queens boss thought his team were destined to nick the win and claim the trophy.
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"The game could have gone either way," he said.
"But, because of the effort we put in to get back into the game, it was just a step too far. We were forced back and a wee bit of tiredness crept in."
However, Chisholm insists extra-time would have benefited Queen of the South more than Rangers' fatigued players.
"I would have liked to have gone to extra-time, I think that would have been a real test for Rangers.
"With us getting the fresh legs on, I would have been quite happy to keep it at 2-2 until the 90th minute and then see how they handled the extra half hour."