Which is the best way to get better/faster on the run?

So I realized after doing my first tri last weekend that the area which needs the most improvement is my run.  Now please realize that I've really only been running for the last couple of months and it is only the last month or so that I've been doing my runs without having to take walking breaks during them.  I'm only doing try-a-tris this years and the runs for the ones that I am doing are 2.5K.  For my training I do between 4-5K and I run the entire time but at a slow pace.  My coach mentioned to me last night that I'm not pushing myself hard enough and that I should do more shorter 2-3K runs at a quick pace to get faster.  So should I be working on getting faster by doing the longer distances and working up slowly over time or run faster for shorter distances now?

I don't have one-on-one coaching - I'm in a group of 20 women that hired a coach to train with us once a week so I really don't feel like she knows what is going on with me as an individual.  She watched me run last night and said while I had good form I didn't look like I was pushing myself (I felt like I was!)  I've been working on mostly getting into a good rhythm and keeping my breathing under control so I don't resort to dropping down to a walk.  In addition to just doing more I guess I'll try and start to mix it up with some shorter runs at a faster pace.  Thanks!