New Zealand trails England 2-1 in the five-game series and must win to keep the series alive.
The Black Caps got into a position to beat England in game three but a middle-order collapse meant the momentum swung towards the visiting side.
Mark Chapman, Tom Latham, Henry Nicholls and Colin de Grandhomme were dismissed within about four overs of each other.
Kane Williamson did his best to drag his team to victory.
The captain made a undefeated 112 but England was able to hold on by four runs.
Despite losing the past two games, Southee said it was not time to panic and the team was confident it could turn the series around.
``The batting effort wasn't anywhere near where we wanted it to be,'' he said.
``But the guys know they didn't achieve what they wanted to in the last game but have all had success at this level, so it is not a soul-searching moment.
``The guys just need to go back and be a bit more clearer in their roles and what is needed at the time.''
To get so close to winning after the match looked like it had slipped away was frustrating. It was also testament to the wonderful skills Williamson brought to the match.
``We probably had no right ... after losing five for 20-odd through the middle.
``But then we saw an exceptional innings from Kane, and aided by Mitch Santner, to get us to within arm's reach [only] to fall short again.
``It was a phenomenal innings. I think the next-highest score - I don't think anyone else got 50 did they?
``To go out and score a hundred and be unbeaten at the end there was a great knock. But I guess it is something that does not really surprise you with how good Kane is.''
The Black Caps are unbeaten in six ODIs at the University Oval and some of the leading protagonists have compiled impressive records at the venue.
Williamson is averaging 53.80 with the bat in five ODIs in Dunedin, while left-armer Trent Boult has really enjoyed the trip south with 12 wickets at an average of 9.41.
He was devastating in the 183-run win against Pakistan in January with five for 17 from 7.2 overs.
Even Southee, who was a bit lukewarm on the merits of Dunedin's weather, conceded the venue had been kind to the Black Caps.
``We have had a lot of success here and I can't put my finger on what exactly it is - maybe it is the weather.
``But we enjoy coming down here ... and obviously we've played some good cricket.''
The big challenge for Southee, Boult and co will be to keep England's long batting line-up on the back foot at a ground where the boundaries are not huge.
``They have some quality players coming in at No8, 9 and 10 that have all scored runs and can really hurt a side. So we know, that as a bowling group, we have to be on song all the way through.
``[Their batting strength] allows them to go harder from a little bit further out as well, so it is challenging as a group but that is the reason why we play the game - to challenge ourselves against the best.
``One of the unique things around New Zealand is the ground sizes vary from venue to venue. It [The University Oval] is no different.
``We've played enough cricket here over the years to know a little bit about the ground.''
