The loss of Denton was keenly felt after the interval as Anthony Foley's side used the driving maul to devastating effect, with CJ Stander and Conor Murray both crossing over through that tactic.
Simon Zebo then touched down to secure a bonus point before Keith Earls added a fifth to ensure Munster moved up to second in the GUINNESS PRO12 on points difference.
But with Edinburgh facing a European clash against Newport Gwent Dragons next week and still in contention for a top-six GUINNESS PRO12 finish, Grant is confident his side can bounce back quickly.
"The better team won," he said. "They played a lot better than us in key areas. Obviously the driving maul, we just couldn't stem it.
"They're a very good driving side, but we knew that coming into it and it makes it all the more frustrating to give away tries like that.
"This weekend's going to be pretty grim and we'll wear it quite badly as you do with any loss.
"It's professional sport. We can't afford to mope around on Monday because it's a huge game next weekend.
"We'll look at things, we'll flush it and we'll get onto the next one."
Click here to see the best images from Munster's bonus-point triumph over Edinburgh
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