Three late goals in four second-half minutes on Sunday saw Rangers close to within nine points of the Dons.
Three late goals in four second-half minutes on Sunday saw Rangers close to within nine points of the Dons with six games remaining in the Scottish Premiership.
Caixinha said it was a "crucial" win, but urged his players to show the same resolve in their remaining fixtures, which will include home games against both Aberdeen and champions Celtic.
"It was a really important match for us. We set this up as the first of seven matches that we must win until the end of the season," the 46-year-old Portuguese said.
"It was crucial. We were facing a very strong side, demonstrated by the beginning of the first half and the beginning of the second half, when they made a lot of problems for us."
"It was just one game, so we need to keep going. Of course it is always important to add confidence, but we still have a lot of work in front of us."
Aberdeen had been on top, but they were made to pay for their profligacy in front of goal when Kenny Miller scored a sublime opener in the 79th minute.
The veteran striker added a second just over a minute later before substitute Joe Dodoo lashed home a third in the 83rd minute.
It ended a run of two consecutive draws for the Gers as they won for the first time in six away games.
It was a welcome boost for Caxinha, who admitted he is still finding his feet in Scottish football just a month after making the move to Ibrox from Qatari club Al Gharafa.
"I'm settled in now, but I'm not going to know Scottish football really until the end of the season," he said.
"I'm getting to know it on a team-by-team basis, but I'm not worried by that."
"I'm assessing what we have in our house. The mentality we need to have and spread at the club -- that is what I am trying to focus on all the time."
The defeat brought to a halt a club record run of 10 consecutive home wins for the Dons, who had claimed 15 victories from their previous 16 games.
"I felt we were the better team throughout, bar a crazy four or five minutes which gave Rangers the opportunity," said Dons manager Derek McInnes.
"Our players have been on a brilliant run and that result is very unusual."
"It's a sore one for us. In the eyes of our supporters that's a huge disappointment and we understand that."
"But while we've lost the fight today it's important we still win the battle for second and hopefully get ourselves into a cup final."