The visitors came closest to opening the scoring but were forced to settle for a point which leaves the hosts five points clear of the bottom three
Rickie Lambert, Steven Davis and Adam Lallana were all guilty of spurning gilt-edged opportunities as Southampton missed out on the chance to further deepen Villa's relegation fears.
The hosts came into the game on a run of four consecutive Premier League defeats and after a difficult week that saw two members of the backroom staff suspended, but will be happy to earn a point as Southampton dominated possession.
Luke Shaw put in yet another impressive performance at left-back, which will no doubt have caught the eye of the on-looking David Moyes in the stands.
The 18-year-old carved out glorious chances for both Lambert and Lallana, but neither could convert as the visitors were left frustrated at having to settle for a point.
Southampton controlled the early stages, Lambert wasting two good chances inside the opening five minutes.
First, Lambert headed Shaw's cross tamely into the arms of Brad Guzan before seeing his effort from Davis' cut-back deflected wide by Nathan Baker's challenge.
Former Villa man Davis was involved again in the 32nd minute, seeing his shot from 10 yards well parried by Guzan after James Ward-Prowse's cross had rebounded off Lambert.
Villa finally showed some attacking intent a minute before the break, Ryan Bertrand's dangerous cross deflecting just wide off Dejan Lovren.
Karim El Ahmadi found some space on the edge of the box four minutes after the interval, but his weak effort was comfortably held by Artur Boruc, back in the side after recovering from a back problem.
Lallana missed a golden chance to break the deadlock six minutes later as once again Shaw proved a threat down the left-hand side.
After breaking clear, Shaw squared for his fellow England international, but Lallana got the ball stuck under his feet with just Guzan to beat and the chance went begging.
In a rare Villa attack, Marc Albrighton stung the palms of Boruc from 25 yards before the visitors had penalty appeals waved away by referee Lee Mason 10 minutes from time when Nathaniel Clyne's cross struck the arm of Bertrand.
It summed up a frustrating day for Pochettino's side, who were left to curse their wastefulness in front of goal they stay eighth, while Villa are five points clear of the bottom three.