A Simon Zebo second-half hat-trick helped Munster run out 51-36 winners at Franklin's Gardens and ensured the visitors earned the top seeding position for the quarter-finals.
"They raised their game from their previous five in the Heineken Cup. They looked after the ball and we gave it away," said Mallinder, whose side finished third in Pool One the season after reaching the final.
"You talk about getting your set-piece right but, while our scrum was good, we didn't get our re-starts right. Our re-starts meant we couldn't get out of our own half.
"You can't just have dominance in the scrum and expect to win the game. Munster dominated every other area and came out on top.
"We played badly today. We got back to within five points in the second half, but then gave away an interception and that was game over.
"We were competing against one of Europe's best sides and, while we did well in Munster and could easily have won, today we came second best.
"What they did very well was slow us down in the contact area. We couldn't get on the front foot and get the ball wide.
"They have a good chance now. They raised their game and I thought they were very good."
Mallinder left out England wing Chris Ashton from his side at the end of a week in which he opted to switch allegiance to English champions Saracens next season.
"You sit down with the coaches and see how they are playing, look at their physical and mental fitness, look at the opposition and then come out with the best 23 players to represent the team," said Mallinder.
"Chris Ashton goes away for the week and hopefully he will get into the England team. That's not a shoo-in, and if he doesn't make it he comes back to us.
"If he does, he will come back in eight weeks and fight for his place in the side. He has been into training this week and worked hard and wants to get his spot back."
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