It's worth considering whether you should disavow links if you haven't seen a manual penalty.
We generally only recommend disavowing links in the following situations:
- For sites that have made links for SEO purposes on a large scale
- For sites that previously had a manual action for unnatural links
- For sites under obvious negative SEO attacks
If you see some weird links you probably do not need to be disavowing links.
When Google takes action either manually or algorithmically against a site for unnatural linking, it's because the site has been actively trying to manipulate Google rankings on a large scale. If you made a couple of directory links in the past, it's currently unlikely you'll get a penalty.
Disavowing a link doesn't take it away so they will still appear as backlinks to your site within the Moz tools. The fact that Google disregards them in relation to your site does not take them off the sites they are on, so best practice is to approach the webmaster first and request the link be removed. If you get no response then disavow.
We always recommend manual investigation of a site to ensure it is a link that is causing harm to your site. When a link is disavowed it can be very difficult to regain that link equity.
To understand how to improve DA (Domain Authority) it can help to get some insight into how we gather our data, which I'll include below. Sorry in advance for the long message!
To calculate DA, we index the web by following links using a crawler. Our crawler is built on a machine-learning based model that is optimized to select pages like those that appear in our collection of Google SERPs. We feed the machine learning model with features of the URL like the backlink counts for the URL and the PLD (pay-level domains), features about the URL like its length and how many subdirectories it has, and features on the quality of the domains linking to the URL and PLD. So, it's not based on any one particular metric, but we're training the crawler to start with high-value links.
In terms of improving your Domain Authority, with the information above in mind, it's best to look at both you on-page SEO to make sure you've covered the basics.
Then you also want to look at your off-site SEO and building more links more links to your site.
There are lots of different areas of Link Building to explore, from patching up broken links, improving your internal link profile, and good ol' fashioned content creation.
Here is a great video by our founder Rand which goes over some easy link building tactics to get you started.
You can read more about disavowing links this here: https://moz.com/blog/do-we-still-need-to-disavow-penguin
Sorry for the long response, I hope this helps!