Two Championship wins this season have been accompanied with six draws and five defeats in the league for Saints, who were relegated from the top flight last season.
Those two victories came on the opening day of the season at home to Wrexham and away at Sheffield United on the final day of September.
After beating Northampton Town and Norwich City in the EFL Cup, they were knocked out of the competition in a 2-1 defeat at Liverpool.
Still’s sacking comes after a run of five games without a win, consisting of two draws and three defeats.
He told Radio Solent after Saturday’s defeat that there was not an “instant fix” for the side after another loss.
“If I’d got an instant fix I would have found it about a month or two months ago.
“I don’t think there is an instant fix to be really honest with you, and I think whoever it is, there’s a big job and I knew there was a big job coming in here.
“I said a few weeks ago there were a lot of things that need to change that haven’t changed yet because we haven’t had the time to do that, but there’s still evidently a lot of work to do.”