The Saints' new regime under the Argentine starts positively with a point at home to the Toffees, with both sides creating good chances but unable to find a telling finish
The Toffees were thankful to keep the first half goalless, as their opponents dominated play and created a number of chances, particularly through Rickie Lambert.
The second period was more even, with the away side perhaps having the best of the play, but neither could take advantage.
The new Saints manager made two changes from the side who drew 2-2 with Chelsea, bringing back Lambert and Gaston Ramirez to the starting XI.
Everton made just one change, with Steven Naismith replacing Victor Anichebe up front, while Kevin Mirallas was fit enough for the bench after six weeks out injured.
Speculation surrounded the home fans’ reaction to new manager Pochettino after his recent appointment but there was a good reception for the Argentine, who showed his appreciation in return.
The home side started brightly and could have taken the lead in the fourth minute as a cross from the right was nearly deflected into his own net by Phil Jagielka.
Jason Puncheon then had a good chance just a couple of minutes later, but he dragged his shot just wide of Tim Howard’s goal.
Saints were playing some decent passing football, and Ramirez almost caught Howard out with a deflected early shot from long-range that the American parried for a corner.
It took until the 20th minute for either side to create another chance, and it came for the home side thanks to Lambert, whose long-range free kick struck the outside of the post.
The former Bristol Rovers man created another chance for himself six minutes later, as he took advantage of some slack defending and forced a good save from Howard after jinking into space.
As the half wore on, Southampton started to increase the pressure, with the influential Lambert seeing a shot cleared off the line then missing a free header as the half ended goalless.
Everton began the second half in a positive frame of mind, with Marouane Fellaini seeing a close-range shot and then a header saved well by Artur Boruc.
They forged a superb opportunity in the 61st minute as a superb ball from Leighton Baines found substitute Anichebe, whose square pass hit Nikica Jelavic’s heel in the penalty area.
Anichebe then had a great chance of his own, as after taking a good touch in the penalty area he saw his shot palmed brilliantly away by the impressive Boruc.
The Nigerian looked lively and caused problems for Southampton’s defenders, releasing substitute Mirallas in the penalty area, who missed a glorious chance for the Toffees.
Despite not creating as much as they did in the first half, the home side very nearly scored a crucial goal in the 83rd minute, as a Lambert header went just over at the back post.
However, neither side could create another clear chance in the dying minutes of the game, so were forced to settle for a point as the full-time whistle sounded.