Sorry, but it looks like some of the answers above address the wrong question.
Yes, manual validation is a must for acceptance, and yes, it usually should be done by people qualified to do it, and ideally working in the same Scrum team. However, the original question was not about that, but specifically about how to treat QA automation under the Scrum framework assuming resource contention. This is much more specific, and something that I also tried solving via different means.
It often happens that automation is an epic in itself, as it requires setting up an environment, developing the framework, code for the tests, the tests themselves, and then hooking up to CI.
Automation can also be expensive, and putting it as success criterion for all development stories can easily grind software delivery to a halt. On the contrary, it is perfectly legitimate to release feature manually tested.
Hence, I don't see any issue with having automation as a separate entity in Scrum.
So, it can be prioritized against other backlog tasks, assuming that the original feature was tested manually, and that the business is happy to pay the price of manual regression testing until automation gets in place. Backlog priorities would depend on how liable the feature is to be modified in the future (and hence require retesting), and how soon will automation provide ROI compared to recurring manual tests.
Bottom-line, this is more of a resourcing question. If you find manual regression price tag constantly growing, and/or defects escaping due to lack of automation, you have a good business case to present to the management: for example to slow down development to catch up on automation, to hire a contractor for a one-off boost to your automation gap, or any other option that the budget can afford.
For example, it is more and more common to find the Software Engineer in Test skillset profile, i.e. people who are both automation specialists and can also pick up development tasks. Having these engineers in the team gives the flexibility to put more emphasis on automation if required. There are other tactics, but as with all real-life situations, there's no silver bullet. For a more detailed answer, I'd need to understand your business's situation a bit better.