A win would have put Real top of the standings on goal difference after Barca dropped their first home points of the season in a 1-1 draw with Villarreal on Saturday.
However, a gritty performance from Osasuna at their claustrophobic Reyno de Navarra stadium and Real's lack of penetration left Manuel Pellegrini's side two points adrift of the champions on 38 with 16 matches played.
Undefeated Barca have 40 points, while Valencia, who beat visiting Espanyol 1-0 on Saturday, are third with 32.
Real Mallorca climbed above Sevilla into fourth with Sunday's 2-0 home win over Athletic Bilbao.
Real were missing the creativity of their injured Brazil playmaker Kaka and chances were scant for both sides in a closely-fought first half in Pamplona.
The visitors showed more penetration in the second period and midfielder Marcelo sent Argentina striker Gonzalo Higuain through shortly before the hour but he skewed his shot wide.
A mix-up between Real goalkeeper Iker Casillas and Spain team mate Sergio Ramos almost let in Walter Pandiani while Higuain was denied moments later by a stunning reflex save from Osasuna goalkeeper Ricardo Lopez.
As the clock ticked down, Real were reduced to taking pot shots from distance and a Cristiano Ronaldo effort after 88 minutes flew just wide from 30 metres.
NEAT CHIP
"We had chances to win the match but our opponents made it very tough for us with their work rate," Real director general Jorge Valdano said in a television interview.
"Our players put in a lot of effort and there is nothing to reproach them about," he added. "There will be plenty of time to catch the leaders."
Earlier, Mallorca beat Bilbao at the Ono Estadi with a deflected Julio Alvarez strike and a neat Aritz Aduriz chip.
After a forgettable first half, Alvarez tried his luck from distance in the 49th minute and his shot looped up off the back of Bilbao defender Fernando Amorebieta and over goalkeeper Gorka Iraizoz into the net.
Aduriz doubled the Balearic islanders' lead after 65 minutes when he raced clear and chipped the onrushing Iraizoz.
Mallorca occupy Spain's fourth Champions League qualifying spot with 30 points, the same total as fifth-placed Sevilla who squandered the lead and conceded a goal in the fourth minute of added time to lose 2-1 at Atletico Madrid on Saturday.
Elsewhere on Sunday, midfielder Francisco Casquero's late strike gave Getafe a 1-0 victory over Real Valladolid which lifted the Madrid club to seventh.
Juan Manuel Lillo had a winning league debut as Almeria coach thanks to Jose Ortiz, whose superb long-range strike in the 89th snatched a 1-0 home win over fellow Andalusians and bottom club Xerez.
Mid-table Sporting Gijon drew 2-2 with relegation-threatened Malaga and sixth-placed Deportivo La Coruna were held to a 0-0 draw at struggling Real Zaragoza.
