Moratti was in the stands for the 1-0 result, which confirmed their progress to the knockout phase of the Champions League.
"These three points took a weight off Benitez and everyone else," said the patron. "Now we have to keep going along this path.
"I saluted Benitez after the game with a handshake and a smile, which are worth a thousand words."
There had been reports Moratti was ready to fire Rafa if he failed to beat Twente, although choices were limited amid an injury crisis.
"We need to make sure the players don't get hurt any more. As for the rest, he is a great Coach.
"We were a little afraid to begin with, but the team really wanted to win and overcame those nerves brilliantly as well as creating many chances.
"We needed the three points at all costs, for team morale as well as anything else. Perhaps we could've scored more, but that is fine, as we played well.
"It was not just grit, but also good football. Now we must continue to do well, match after match. It has to be said that it was absolutely crucial we progress in Europe."