The Ibrox side were outclassed by their Glasgow rivals, only really threatening in the closing stages while 2-0 down.
Caixinha also admitted he changed his pre-match team talk on the advice of assistant Helder Baptista to ease tension among the players.
"By respecting the opponent we dropped off too much. It wasn't what we prepared during the week," he said.
Caixinha said he did not believe his game-plan had been unclear to his players, but he gave an uncommon insight into his pre-match approach.
"Helder came to me just at the end of the warm-up and told me 'please, in your speech, don't be so tough. They need to feel a little bit more freedom'," the Portuguese added.
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"When you don't feel that freedom you don't enjoy and you don't perform the way you need to.
"We were a little bit 'blocked' and if you're blocked - even if you have the best organisation and the best ideas - you can't perform."
Caixinha said Baptista felt the players were tense, but stressed he did not believe they were frightened by the occasion or their opponent.
The Portuguese was asked about his tactics for the game, prompting a detailed response, outlining what he had hoped his players would execute.
"We organised our defending in three ways. The first one was to try to place a high block - if you see they were trying to build from the back - they open the centre-halves and Scott (Brown) is always in the middle. We had three players down there," he explained.
"In the middle of the park what we were trying to get them to play the ball to (Mikael) Lustig, block it, block Brown who was making the triangle with the centre-halves, and with this block we could have space to explore after we regain possession.
"We could not do it in this match because we were a little bit lower on the pitch. In the lower block, we were expecting not to allow them to divide the game.
"We just played wide when the spaces were inside. The idea was for our wingers to come inside and fill the space."
Despite seemingly thorough planning, Caixinha accepted his strategy had failed to work.
"The game-plan is one thing, what we put in practice was a totally different thing," he acknowledged.
"So it wasn't our day. We couldn't perform the way we prepared. We expected more from our players but we need to keep going.
"After tomorrow's day off we need to get back to Murray Park to start preparing the next match and we still have five matches to go until the end of the season."
Pedro Caixinha felt his Rangers team gave Celtic too much respect as they lost the Scottish Cup semi-final 2-0.