specification by example
http://specificationbyexample.com/resources.html
http://www.infoq.com/articles/specification-by-example-book
When my current team first implemented agile, we also didn't have any automated regression tests. We released every two weeks. We spent the last two days of each release having everyone on the team divide up and execute the scripted manual regression tests. This was great motivation for every developer to think about good ways to solve test automation problems.

Test automation is simply a part of software development. It isn't a separate activity. The same people who write production code also must write test code. The testers specify what test cases to automate, the inputs and expected results. There are many ways to accomplish this.

I highly recommend Gojko Adzic's book Specification by Example, http://specificationbyexample.com, as a starting place for your entire development team (or all your teams if you have more than one) to start learning how to achieve a sustainable pace along with high quality code by integrating testing into coding.

Of course, there are other testing activities where testers' specialized skills will contribute value, such as exploratory testing. But you won't have time for that if you force testers to try to solve regression testing problems by themselves.

You probably have lots of problems at this point. It takes a long time to find ways to improve your development. Get everyone on your team together for a retrospective, identify your biggest problem, think of some small experiment that will help make the problem less bad, and try it. Then see how that worked, and continue on.
-- Lisa