It is not so much the numbers that matter (although numbers matter too), but what you do with those numbers.  Before Gen Petraeus, the emphasis used to be on "force protection" (as characterized by various Force Protection Levels) ~ minimizing US casualties.  Unfortunately, "force protection" is oftentimes inconsistent with "securing the population" and "living with the people".  The US forces were very good at setting up very well protected bases, and they were very good at traveling from one base to another base in large armored convoys at high speeds.  This scenario builds up a lot of resentment in the population, and paints a large bulls-eye on the occupying army.  Gen. Petraeus talks about a "liberating" army quickly transitioning into an "occupying" Army... and the heavyhanded emphasis on force protection no doubt hastened that process.  "Force protection", ironically, is counterproductive to force protection.

With the adoption of the Petraeus doctrine, the emphasis shifted to "securing the population", and ensuring the safety of the average Iraqi.  To be sure, "force protection" is still a component, but it is no longer the only component in the equation.

Gen. Petraeus outlined his doctrine in a widely read article called Learning Counterinsurgency: Observations from Soldiering in Iraq (warning: pdf file).  Here are some observations that he lists:

1."Do not try to do too much with your own hands."

2. Act quickly, because every Army of liberation has a half-life.
   
3. Money is ammunition.
   
4. Increasing the number of stakeholders is critical to success.
   
5. Analyze "costs and benefits" before each operation.
   
6. Intelligence is the key to success.
   
7. Everyone must do nation-building.
   
8. Help build institutions, not just units.
   
9. Cultural awareness is a force multiplier.
   
10. Success in a counterinsurgency requires more than just military operations.
    
11. Ultimate success depends on local leaders.
    
12. Remember the strategic corporals and strategic lieutenants.
    
13. There is no substitute for flexible, adaptable leaders.
    
14. A leader's most important task is to set the right tone.
    

On the first point, he cites TE Lawrence who said

Better the Arabs do it tolerably than that you do it perfectly. It is their war, and you are to help them, not win it for them.  Actually, also, under the very odd conditions of Arabia, your practical work will not be as good as, perhaps, you think it is. It may take them longer and it may not be as good as you think, but if it is theirs, it will be better.  

On the second point, he states that every liberating Army quickly becomes an occupying Army.  The duration for this process depends on the perception of the local people, and on the attitude of the liberating/occupying Army.  He says that by 2004 (when he last served in Iraq), the US military had become an occupying Army.  He left it unsaid, and so I am reading between the lines in concluding that this transition was hastened by the previous emphasis on "force protection"

Point number 4 (increasing the number of stakeholders is critical to success) should have been obvious, but was not realized by the leaders until well after the war had been initiated... instead, an emphasis was given to "winning hearts and minds" (which is important for other reasons, such as extending the shelf life of the "liberating Army") at the cost of ensuring that more Iraqis had a stake in an Iraqi future.

Point number 4 (analyzing the cost and the benefit of each operation) was framed in a simple question:

"Will this operation," we asked, "take more bad guys off the street than it creates by the way it is conducted?" If the answer to that question was, "No," then we took a very hard look at the operation before proceeding.

Notice the emphasis in this question is whether it takes bad guys off the streets, not whether it minimizes US casualties.

Let me skip to point number 9: Cultural awareness is a force multiplier.

Cultural awareness is a force multiplier, reflects our recognition that knowledge of the cultural "terrain" can be as important as, and sometimes even more important than, knowledge of the geographic terrain. This observation acknowledges that the people are, in many respects, the decisive terrain, and that we must study that terrain in the same way that we have always studied the geographic terrain. Working in another culture is enormously difficult if one doesn't understand the ethnic groups, tribes, religious elements, political parties, and other social groupings--and their respective viewpoints; the relationships among the various groups; governmental structures and processes; local and regional history; and, of course, local and national leaders. Understanding of such cultural aspects
is essential if one is to help the people build stable political, social, and economic institutions.
Indeed, this is as much a matter of common sense as operational
necessity. Beyond the intellectual need for the specific knowledge about the environment in which one is working, it is also clear that people, in general, are more likely to cooperate if those who have power over them respect the culture that gives them a sense of identity and self-worth.

He concludes by saying

It goes without saying that success in Iraq--which clearly is important not just for Iraq, but for the entire Middle East region and for our own country--will require continued  military operations and support for the ongoing development of Iraqi Security Forces. Success will also require continued assistance and resources for the development of the emerging
political, economic, and social institutions in Iraq-- efforts in which Ambassador Zalmay Khalilzad and General George Casey and their teams have been engaged with their Iraqi counterparts and have been working very hard.
Lastly, success will require time, determination, and resilience

I would suggest reading the whole article...it is quite fascinating.