Probably the opposite.

Our "higher reasoning" and "state of awareness" (needs defining) gives us the ability to do thigns other animals can't. For example chronic pain sufferers are taught how to manage their pain with a variety of CBT techniques. Not something you can teach a dog or cat.

People in intense periods of intense suffering may have thw ability to dissociate from the experience ("go to their happy place") to lessen the pain experience.

We're not aware animal shave this ability.

If anything mammals of all kinds that feel pain don't have our higher cognitive ability to help manage and supress it.

Having said that it's possible we feel more emotionally complex pain. Pain induced from our own minds by remembering trauma or imagining painful situations. As someone pointed out below a dying animal probably isn't thinking about the loss of it's family as it's dying. But it will be feeling the pain of dying acutely.

I wrote my compiler in Haskell because it seemed that it’d be much less hassle compared to do it in a object oriented or procedual language.

That is not a feeling I'd associate with Haskell!!

"I didn't put a WHERE clause in that DELETE statement"