A late Clint Hill equaliser secured a 1-1 draw at Celtic Park and Murty said the team had proved a point.
"I'm pleased for the players," he said after his last game in charge. "They showed the kind of tenacity and grit that they've been questioned about.
"It's a difficult environment, but two outstanding saves from Craig Gordon or it could have been more."
A Celtic victory would have been their 23rd in succession in the league and their 18th in all competitions.
The Premiership leaders took a first-half lead thanks to Stuart Armstrong's well-taken goal.
Rangers, in front of their new manager, Pedro Caixinha, who was watching from the stands, continued to battle and were rewarded with Hill's 88th-minute goal.
"He saw the players deal with an unbelievable atmosphere," Murty said.
"It takes a real man's performance to play in that and stand up to it.
"I'd been challenging them all week, saying you're the only ones who believe in yourselves.
"They showed that right to the end and I'm proud of them.
"From the moment I saw them at breakfast, I knew they were right where I wanted them to be."
The two Glasgow rivals will meet again in the Scottish Cup semi-final at Hampden Park on 23 April.
Murty, who had gone into the league game with a record of three wins and two defeats in his previous matches in charge, hands over to Caixinha with the side sitting third in the table.
"This should give them lots of confidence," he said.
"They didn't get rattled or lose their discipline.
"We made it difficult for them and put a shift in."
Caixinha will hold a staff meeting at Rangers' Auchenhowie training ground on Monday as he begins his spell in charge of the first-team.
In a message on Rangers' Twitter account, he urged fans to back the team.
"We are doing our very best, in a club like this, to keep up a track of winning," said the Portuguese manager.
"We want a winning mentality. We want a winning team. And you [the Rangers supporters] need to be here to support us."
Murty is expected to return to his role as head coach of the development squad.
Rangers caretaker Graeme Murty praised his players for answering their critics as they ended Celtic's winning streak.