Real had scores of chances at the Molinon against a team with a fraction of their resources but could not find a way past Gijon goalkeeper Ivan Cuellar, the likes of Cristiano Ronaldo, Gareth Bale and Jese all drawing a blank.
James Rodriguez made little impact when he replaced Jese in the second half, while fullbacks Danilo and Marcelo were largely ineffective when they attacked down the wings.
"I knew it was going to be a match in which Sporting made things hard for us," Benitez, who has had stints at clubs including Liverpool, Chelsea and Napoli since leaving Valencia in 2004, told reporters.
"There were a lot of shots but without precision and in the first half we allowed them to get into the game," added the 55-year-old, who has taken over from the sacked Carlo Ancelotti.
"We have to improve things, we have to work more. We were lacking the final pass and skill in our execution in attack."
Real are hoping to improve on a 2014-15 season under Ancelotti in which they failed to win the Champions League, La Liga or the King's Cup.
Benitez has returned to club where he featured as a player and coach in the youth academy and is seeking to deny arch rivals Barcelona, who won the treble last season, their sixth La Liga title in eight years.
Barca got their La Liga campaign off to a winning start earlier on Sunday with a 1-0 success at Athletic Bilbao.
Benitez said his players had reacted well in the second half against Gijon and that he remained upbeat about Real's chances of lifting silverware this term.
"The players showed character and personality and in the second half were clearly going after the game," he told reporters.
"What I have clear in my mind is that this is just the beginning," he added. "We have to keep making adjustments. I am still optimistic."
(Reporting by Iain Rogers, editing by Ken Ferris)
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