Despite the return of Ireland internationals Stockdale, McCloskey and Nick Timoney, Ulster struggled against a powerful display from Munster in the first half as tries from Alex Kendellen (2), Marnus van der Merwe and Dan Kelly put Clayton McMillan’s side in the driving seat at the break.
But despite a spirited second-half showing to earn another three points after last week’s draw in Glasgow, Murphy said he was “bitterly disappointed” when asked if he was left with mixed emotions.
“We allowed Munster to set the tempo, we were inaccurate with our first launch, so that we kicked off, they kicked out, so we were inaccurate with that first launch,” added Murphy.
“Off the back of that, penalty, penalty and then you’re back in your corner and fighting for your life.
“Once you’re five metres out and the opposition have a line-out, it’s very hard to stop, so that gave them control of the first half.”
Having pegged Munster back, Ulster could have won the game with the final play, but Robert Baloucoune’s attempted pass to Matthew Devine was cut out by Alex Nankivell as the hosts’ winless URC run stretched to seven games.
“Coming in at half-time, I thought the lads reacted really well,” added Murphy.
“We made some changes, still very inaccurate in the second half and didn’t look after the ball well enough, didn’t control field position at all in the game, but ultimately we got into a situation where last play of the game we were running at them and gave them the ball back again.
“Our turnover rate needs to come down, our scrum has been going really well but took a backward step tonight and I kind of feel like we didn’t attack the game the way we needed to.”
Munster boss McMillan was similarly downbeat after his side were held scoreless in the second half to let slip a 21-point advantage.
“We talked about it at half-time that Ulster are a quality side that won’t go away,” he said.
“We needed to continue to be accurate and just apply pressure in the right parts of the field.
“But we didn’t quite get the same quality of possession in the second half, and Ulster were good enough to find a way back into the game.”