"There's no real satisfaction in terms of how we played and our approach. I thought we had some good performances.
"Maybe I expect too much from us at times and I expect us to be better and defend better."
Rangers went ahead through Steven Davis and Lee McCulloch followed up with a second before the break.
We're just desperate to get back here and have another go at it
St Johnstone manager Derek McInnes
And, although the Perth side pressed for much of the second half, they failed to create many clear-cut chances.
"Rangers are through because they took a couple of opportunities and they defended better throughout the game," said former Rangers midfielder McInnes.
"I thought we had some really good performances, but I do think certain the goals were very, very poor and ultimately that's cost us."
Murray Davidson missed a good chance to put Saints ahead when he headed wide.
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"Nine times out of 10, you would expect him to hit the target and possibly get a goal from there," said McInnes after Saints lost their fourth semi-final in three years.
"We're just desperate to get back here and have another go at it."
Source: BBC Sport
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