You certainly can! This might sound confusing, but you should use the IFTTT webhook trigger for that.
Set it up however you need to for your custom service, then provide the resulting URL to the service you're using. The URL isn't restricted to IFTTT, it was just originally intended for IFTTT but can be called from anywhere. You could even just paste it into your web browser and it will trigger your sequence.
With this in mind, it's best not to share these URLs publicly otherwise anyone with the URL can trigger your sequence. If this does happen and you need to reset your secret key, contact us and we can help you out.