Unless you're a technical specialist like a surgeon, you serve your team, not the other way around. Your organizational reason for being is to make your people more effective. To pay for you, their collective output has to increase by more than whatever you cost. So you need to serve them before doing anything else by making sure they have what they need to perform.
Here's how I do that: first thing every morning I walk around and talk to all of my direct reports. We talk about the day's work and anything that might keep them from getting it done. I fix what I can during the walk-around, and address the rest as soon as I get back to my office. Then I finally look at e-mail and get to my own work.
The last 30 minutes of my day is set aside to review tomorrow's work and verify that my team has the necessary resources to do it.
Bottom line: My team's productivity is more important than mine. If they fail to perform, it's on me as the leader. And then it doesn't matter how much I personally got done, my team (I) still let the organization down.