The Ibrox boss watched his new team slip 12 points behind the Dons after a frustrating 0-0 draw away to Kilmarnock.
With just seven games remaining, time is running out for Gers to snatch second but they do still have to play Derek McInnes’ men twice - starting with this weekend’s Pittodrie encounter.
And Caixinha has now laid down the gauntlet to his team.
“It’s getting difficult,” admitted the Portuguese coach. “We know we need to play twice against Aberdeen and that they have to play against all of the top six again.
“The maths says it can still be done but the next game will be crucial to understand if you are able or not.
“If you don’t win Sunday against Aberdeen, you don’t deserve to be in second position. But that is my challenge. It is something we need to prove to ourselves.
“We are Rangers. We want to fight. At this moment, this is the challenge we need to try and fight for at the moment.”
Gers were largely on top at Rugby Park but, despite seeing a Joe Garner header hit the crossbar, they were held to an Ayrshire stalemate for the second time this season.
It came after Caixinha took the unusual step of naming his starting line-up a day early.
With five defenders missing he stayed true to his word and put out the same 11 he named during his pre-match press conference, with youngsters David Bates and Myles Beerman making their debuts.
Killie interim boss Lee McCulloch admitted he tinkered with his gameplan after learning of Caixinha’s team.
But the Gers manager insisted giving his players - especially his two academy graduates - his backing was more important than the element of surprise.
“Sometimes you might be bluffing but I am not a bluffing guy,” he stressed. “I need to give confidence to my team.
“That was the message for the opponents and for all of Scotland, but it was especially a message for our players to say that I am counting on you.
“It doesn’t matter which 11 we have. Let’s go to war.
“Would I do it again? If I need to do it, I will do it for sure.”
However, Caixinha was left deflated by the result, admitting: “It’s not enough, we are Rangers, we have a culture of winning and getting the three points all the time. So we cannot be happy drawing the game.
“We need to be reinforcing the players the demands of playing at such a massive club who needs to win all the time and we need to be angry when we don’t do it. We should be angry that we didn’t and that’s the frustration.”