Ulster head coach Dan McFarland said it "took every ounce" to keep Munster out in the closing minutes of Friday's 21-14 win at Kingspan Stadium.
Ulster fought back from 14-3 down to inflict a first defeat of the season on the United Rugby Championship holders.
McFarland said it was "a pretty big ask" to fight back and hold off as Munster pummelled the Ulster line in the closing stages in Belfast.
"I was really pleased with the way we fought back into it," McFarland said.
It looked like Ulster were suffering from a hangover from their defeat by Connacht as inter-provincial rivals Munster dominated the power game and Craig Casey's two tries, both off the back of strong work by the forwards, put the visitors in a strong position.
Their second try was even more impressive given they were playing with 14 men after Shane Daly was sent to the bin for a tackle on Ethan McIlroy, who was knocked unconscious and taken to hospital. McFarland added that the tackle by Daly "wasn't malicious".
Ulster hit back when Jacob Stockdale's gamble to let Billy Burns' kick into the corner take a bounce paid off as he gathered the ball and raced over in the corner.
Nathan Doak kicked Ulster level from the tee after the restart before McFarland's side moved ahead when Nick Timoney touched down, aided by the returning Ireland duo of Rob Herring and Iain Henderson, along with impressive debutant prop Scott Wilson.
Munster harried the Ulster line in the closing stages and Henderson produced a superb tackle to hold Scott Buckley up over the line, as the hosts held on to secure a memorable win.
"I was pleased with a lot of what we did in the game. We showed some real attacking intent and we were really dangerous.
"It would have been nice when we got back into it and were seven points up that we could close the game out with a bit of composure, but I don't know if the guys wanted to demonstrate their fighting spirit for the last five minutes of the game. They certainly did that.
"It's a credit to Munster that they are the type of team who will never say die.
"You never come across a Munster team that gives up the ghost at the end of the game. They were battering away at the end like they have done on so many occasions.
"It took every ounce that we had to stop them scoring."
'We don't like to lose'
Ulster headed into the game off the back of a late and narrow defeat by Connacht in Galway. McFarland stressed that bouncing back was "important" as he looks to make the Kingspan Stadium a fortress in the new campaign.
"We don't like to lose at home. Well, we don't like to lose anywhere but particularly at home," he added.
"We lost at home last year to Munster in the corresponding fixture having beaten them away from home. It was really disappointing and the guys were gutted about that.
"They are always hard-fought, but we took a lot from last week. There were a lot of guys who had less time on the field who played down in Connacht, against a team who I felt were playing the best rugby in the league at that point.
"We put up a really good fight. We didn't come away with a win in the end, for whatever reason, but I was pretty proud of their efforts last week.
"A lot of what we are doing at the moment is not as neat and tidy as we want it to be, but it's game four so why would it be?
"I also see a lot of what we practiced over the summer and we're pretty dangerous as well."