Budimir converted a penalty at El Sadar to settle a bad-tempered contest, taking Osasuna to seven points from their opening three matches of the LaLiga season. Getafe had a first-half equaliser ruled out and finished the game convinced they had been harshly treated by the officials.
Head coach Luis Miguel Ramis praised his side's mentality after a physically demanding week.
"The team wants it, has soul, has character and is intelligent as a collective," he said. "The most important thing is that the team understands what we want from them, and in every match they've interpreted very well what needs to be done."
Ramis explained that Osasuna deliberately avoided pressing too high against a Getafe side built to play direct and contest second balls.
"It was absurd to jump players forward because then you'd have to retreat," he said, adding that his team controlled possession in the first half before fatigue forced a more reactive approach after the break.
"When your body doesn't give you its best, or you run out of energy, the best thing is to shelter, stick together and make things difficult" for the opponent, he said, noting Osasuna have conceded only once in three league games. "That's the line," he added, saying he wants goals against his side to come from opposition quality rather than poor organisation.
On the injury front, Ramis said Jorge Herrando has an adductor problem while Aimar Oroz is struggling with his hamstrings, with Herrando's issue appearing "more serious" pending medical tests. Asked whether seven points from nine offered room for optimism, he was cautious.
"Feet on the ground and eyes on the moon — if we have to go on a trip, let it be matchday 38, I wouldn't dare after just three," he said. He also suggested Osasuna's business in the transfer market was not finished. "I think there'll be another addition," he said, while ruling out departures before Tuesday's deadline.
Getafe boss José Bordalás was left frustrated by the result, insisting his side had done enough to avoid defeat.
"We're hurting. I don't think we deserved the loss — we were much the better team, but the details decide matches," he said. "We've had three games now where we've been penalised by a sending-off and two very harsh penalties."
Bordalás was particularly aggrieved by the penalty award against his side, believing a foul on Djené went unpunished moments earlier.
"There's a clear foul on Djené that gets ignored, and we're not used to it, but... you be the judge, it doesn't surprise us," he said, adding that Getafe are treated differently to their opponents by referees. On his squad's fitness, he confirmed only Andrés García had picked up a knock, and hoped late reinforcements would arrive before the deadline.
He also paid tribute to goalkeeper David Soria's appearance record for the club: "Achieving it shows the level of commitment and professionalism — we're delighted for him above all."