The Magpies put in a lethargic display at St Mary's and can have few complaints at having found themselves on the wrong end of a Premier League thumping.
They allowed the hosts to dominate throughout and could have succumbed to the incessant pressure long before the Saints' stoppage-time opener at the end of the first half.
Part of the reason that Alan Pardew's side were able to hold out so long was the performance of Elliot, but he concedes that as a collective the Magpies were well short of their best.
He told Sky Sports: "We have to hold our hands up, it wasn't good enough from us today.
"Southampton played well and we just didn't rise to it. It's very disappointing from our part. Maybe three games in a week (hasn't helped), but it's no excuse, we just didn't turn up.
"They just started a lot quicker and got on top of us and we didn't really get into the game until 25 minutes in.
"It's a tough place to come and we're disappointed with the way we played. We knew what they were going to do but unfortunately we couldn't quite handle it today."
On his own performance, which saw him make a string of fine saves, Elliot added: "It's a lot better when you haven't conceded four, but the important thing is getting results as a team and building the season, because we've had a good season so far.
"Personally, it's good to make saves but ideally you want to come off the pitch a winner."
Newcastle have now lost three of their last four in the league and know that things are not about to get any easier as they ready themselves for a visit from Manchester United next weekend.
Asked about how they will prepare for that contest, Elliot said: "We don't want to get too down because our recent form hasn't been that bad.
"We've had two bad defeats, but we have to go back to the drawing board, work hard in training all week and whatever team the gaffer puts on the pitch will have to give 100 per cent. Any game against Man United is always a tough game."