Pena was substituted eight minutes into the 2-0 loss to bitter rivals Celtic after looking off the pace since his arrival at the club in the summer.
Caixinha admitted at the start of the season that it may take a bit of time for the Mexican to get used to the demands of the Scottish Premiership, but denied that he made the substitution as a result of Pena struggling to keep up with the pace of the game.
The 27-year-old was put on an individual training programme at the start of the season after a sluggish start to his Ibrox career and - although he appears to have made little progress - Caixinha denied reports that he criticised the player following the defeat.
He said: “I didn’t say that after the game. When I was young, the boys used to call me elephant, because elephants have a great memory and I have a great memory. I know what I say and the moment I say it.
“I said that (he was struggling to reach the right fitness levels) about Carlos when we had the team picture at Ibrox, and I said Carlos would need to improve at that moment in time. I never said it after the match.
“In that specific action we identified that he needs to improve - he still needs to improve.
“We know the type of player we have and the work that needs doing.”
However he added: “Decisions have nothing to do with fitness. I can show you the data that we have on a daily basis that is the total distance covered and the high intensity runs the players do.
“I can tell you that for a long time, Carlos is in the top three of that list.”
Experienced defender Bruno Alves looks to have shaken off a thigh problem and is in contention to return to face Hamilton on Friday night.
“Bruno after the three days he spent in Madrid, he arrived (in) very, very good (condition),” he said.
“He arrived much better than he left, so he is still with the physios trying to recover.
“We think it is still possible (he plays on Friday) but we need to check and keep assessing.”
Fellow defender Declan John has also been cleared to return after he also suffered a thigh problem and was forced to miss the derby.