Sociedad came into the game targeting a third straight win, but had to settle for just a point, despite edging a disappointing match.
Philippe Montanier's side, 2-1 victors over Malaga a fortnight ago and 4-0 winners against Rayo Vallecano on Monday, could have gone sixth with victory, but they draw a blank against the league's second-bottom side.
As it was they remained ninth, while their opponents moved to within a point of safety.
The hosts, as expected, started the stronger and Antoine Griezmann should have done better than shoot wide from well inside the area.
At the other end Nano met an Emiliano Armenteros delivery, but his header was punched clear by goalkeeper Claudio Bravo.
Sociedad were showing few signs of the form that had lifted them into the top half, although Diego Ifran sent a header over the top.
And the hosts continued to struggle to get into their stride after the break.
Carlos Vela saw a shot from close range tipped over the top by Andres Fernandez 10 minutes into the second half before Ifran fired wide.
The Uruguayan striker was becoming increasingly involved but still could not find his range, heading wide from six yards with his next attempt.
He sent another shot over the top before Osasuna had two late chances to stun the hosts.
Roland Lamah got a shot in well inside the area and Bravo had to be alert to block it.
Bravo then was in the right place to hold a David Timor header as the match ended goalless.