Clayton McMillan says Munster "stood up when it really mattered" as they narrowly avoided a first defeat of the season.
The hosts trailed for most of the match against an ill-disciplined Edinburgh side, who had four men sent to the sin-bin for a variety of illegal challenges.
Andrew Smith scored a try in the second minute but the visitors, despite losing two players at the end of the half, looked more dangerous and led 19-10 with just over 20 minutes to play.
Michael Milne scored a try in either half for the hosts, while Fineen Wycherley's 72nd-minute try secured a 20-19 bonus-point win.
Munster, who made 10 changes to the starting side that beat Cardiff, had to hold out a late Edinburgh attack that almost put the Scottish side in position for what would have been a potential winning kick.
"Aspects, there was some stuff that we talked about last week that we weren’t so good at and I think we showed some improvement," McMillan (above) told TG4.
"The real pleasing thing was that we had a number of new bodies and they all acquitted themselves well.
"We got put under immense pressure and stood up when it really mattered so those bits are really encouraging.
"Lots to work on, it’s only game three.
"The changes mean that you lack a little bit of rhythm but the trade-off is that you are getting bodies out there and they are all fighting to get out there the next week.
"And at this stage of the season that’s just as important.
"We know that we need to be better but we’ve shown we aren't going to roll over and die easily so that is hugely encouraging."
McMillan, who joined from the Chiefs over the summer, had left out-half Jack Crowley out of his squad to comply with IRFU player-management rules and was also without injured scrum-half Craig Casey.
On the union protcol, he said: "I’m accustomed to it and I’m actually in favour of it.
"It’s about having your best players available for the duration of the season.
"They end up playing lots of games through internationals and their clubs. We rely on them heavily so we need to do what’s best for them."
Munster are joint top of the table with 14 points and face Leinster, who play Sharks today at 5.30pm, next Saturday at Croke Park.
"[I’m] looking forward to it but I think we want to celebrate tonight," said the New Zealander.
"This is a tough team that we played.
"We managed to get across the line so we’ll celebrate that first and the boys can enjoy a weekend off, and then we’ll come in and turn our attention to Leinster next week."
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