A betta likes little current. Just because the fish was found stuck to the filter doesn't mean the filter killed it. Whatever the reason it died, it would eventually end up sucked against the pipe if you had not noticed it earlier.
You can put a piece of sponge on the end of it if you like. You can buy sponges that fit over filter pipes anyway as people who breed fish often use sponge filters so the replacement sponges, which you can shove onto the end of various filters, are readily available in pet shops.
How long have you had the tank set up and how many fish do you have in it? If not cycled, the fish would have died from poor water conditions. Bettas are not a good addition to a new tank as they prefer a mature set-up.