Add the tomatoes, onion, carrot, and garlic to the Instant Pot. Sprinkle the oregano, basil, and salt over the top of the vegetables, but don't stir. (You don't want the seasonings to touch the bottom of the Instant Pot or you could get a burn error.)
Secure the lid and move the steam release valve to Sealing. Select Manual or Pressure Cook (the name of the button will vary by machine) and cook at high pressure for 20 minutes. It will take roughly 10 minutes for the pressure to build in the pot before the cooking cycle begins, so the pot will say "On" until then.
When the cooking cycle completes, allow the pressure to naturally release for 10 minutes. When the screen reads L0:10, move the steam release valve to Venting to release any remaining pressure. When the floating valve drops, it's safe to remove the lid.
Use an immersion blender to blend the cooked vegetables into a smooth sauce. Add in the tomato paste and blend again to make sure it's fully incorporated. It should thicken the sauce. Adjust any seasoning to taste, then serve warm over your favorite pasta.
This sauce should keep well in an airtight container for up to a week in the fridge, or you can freeze it for up to 3 months.