This exchange gives us our first glimpse at M's priorities—the data, and her country, over the lives of individual agents. The agents who live, like Bond and Silva, resent M for her decisions. Bond is able to get over it, but Silva cannot, and the entire plot of this movie revolves around his attempt at payback.
M: I made a judgment call.
BOND: You should have trusted me to finish the job.
M: It was the possibility of losing you or the certainty of losing all those other agents. I made the only decision I could and you know it.
BOND: I think you lost your nerve.
M: What do you expect, a bloody apology?
M and Bond argue over who they should be loyal to—the country or the agents. As an agent, Bond wants to be on the side of his comrades. But M has the bigger picture to think of, and sometimes she must sacrifice her agents in the name of loyalty to her country.
M: Because we're under attack. And you know we need you.
Even though Bond was almost killed because of M's decision, he returns to work for MI6. Why? It isn't because he needs the paycheck. He returns to work out of loyalty to his country.
M: Find out who he works for and who has the list. Then terminate him, for Ronson.
Here M demonstrates that she isn't the heartless old bat some may have thought her to be. Even Bond may have thought that, temporarily. She has sacrificed an agent for the greater cause, but she feels a sense of loyalty to that agent's memory.
M: I f***ed this up, didn't I?
BOND: No. You did your job.
Bond and M come to a point of forgiveness when Bond realizes that M's loyalty to England is greater than anything else in her life. Bond knows he can't take it personally if he's second banana to Mother England.
MALLORY: Are you ready to get back to work?
BOND: With pleasure, M. With pleasure.
After M's death, her Union Jack-covered dog is passed to Bond. This gift—and the memory of M in general—is an incentive for Bond to take up her mantle and fight for England at any cost…as if he weren't doing enough already.