Leicester head coach Matt O'Connor was left to rue his side's lack of precision but described Munster as "cynical" as the Premiership outfit fell to a 33-10 defeat at Thomond Park.
After building a 23-3 half-time lead thanks to tries from Rhys Marshall and Simon Zebo, Peter O'Mahony and Chris Cloete crossed for the hosts in the second period either side of Harry Thacker's consolation.
Munster have moved four points clear of Castres Olympique and five clear of Tigers in Pool 4 ahead of their return game at Welford Road next weekend.
O’Connor knows there is room for improvements but felt that Munster "killed the ball" at every opportunity.
"We were inaccurate," he said. "You cannot come here and be inaccurate.
"They were very diligent and cynical - they killed the ball whenever we had opportunities"
"I thought we were poor, we didn't look after the ball well enough and we turned over the ball 20 times.
"Munster took their chances in the first half, they were very clinical and accurate. From there, they were very diligent and cynical - they killed the ball whenever we had opportunities.
"That made it hard for us to score. It's always the same here, you have to make sure you are accurate. They are very committed and you have to be more accurate."
Despite the heavy nature of the defeat, the Australian is looking forward to Sunday's must-win return fixture.
"Without stating the obvious, next Sunday's game is really important," he added.
"The boys are always excited at Welford Road. They play with a lot of passion there and we're going to have to make sure that we put out a performance that gets us the result and puts us back on an even keel in the group.
"We have made some good strides, but we have to make sure that we fix it this week."
His counterpart South African Johan Van Graan will be acutely aware that having demolished Leicester 38-0 at Thomond Park at the same stage of the competition last season, Tigers bounced back to win the second of the back-to-back fixtures, 18-16, just a week later.
Van Graan, who has taken over from Rassie Erasmus, South Africa's new director of rugby, said: "I thought we started the game pretty well, very happy with the win first and happy with the bonus point. There are a lot of areas we can still improve.
"I thought the guys responded well to what we did in the week and what we planned. We will enjoy the win.
"Like I said last week, you never take a win for granted and come back on Monday and start again at zero.
"We knew this was going to be a big clash, two of the best teams in Europe. Just look at the history between the two clubs.
"Both sets of forward packs brought their physicality and fair play to the backs who put their bodies on the line both ways. It was a very good game of rugby and I'm very happy with the win."