My belief is that Pete knew he had some expectations this season and he knew he wasn't meeting those expectations. The single most telling event that indicates such, to me, is the Leonard Williams trade. It's a trade that sticks out as different than any other in the PC/JS era. As a relatively high cost/short-term benefit, mid-season move, I think it shows Pete knew he needed a change ASAP. That move didn't improve the pass-rush nor the run D so....
I'm a fan of Pete Carroll. Many here have been saying, "the game has passed him by" or similar, for a few years. To that point, he has always valued DB play over pass-rush. There's been more investment from the draft and FA in the backfield vs relying on relatively cheap FA DL/Edge used in rotation. As the league has disadvantaged DBs and as on-field calls have done the same, the game has tipped slightly away from Pete's philosophy...making it harder for his team to consistently win.
I believe, last season he was given an ultimatum to prove it still works and he started the season with confidence he could: healthy JAdams and Riq Wollen coming off a great season. When it wasn't playing out that way, he brought in Leonard Williams as a Hail Mary.
To the topic of the thread, if any of my thoughts above are accurate (and they may very well be flawed) I don't think the decision was made solely on W/L record or making the playoffs or playoff wins. I think it really was a "football decision". I don't think one win would have made a difference.
I hope he sticks around to advise, especially with his hand picked DBs. If the new regime (relatively) heavily invests in Edge this off-season, I'll see it as a sign some of the above hits a mark.