Queen of the South paid for a month without a competitive game as they lost the Scottish Cup final, according to manager Gordon Chisholm.
His side had to arrange friendly games after the First Division season ended.
"Rangers were worthy winners," Chisholm said after the 3-2 defeat. "But going into the game without four weeks of competitive football showed.
"We did not turn up in the first half. The second half was more like us and I can be nothing but proud of my team."
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.
"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."
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