Both sides had spurned golden opportunities but a lack of quality in the final third was the enduring theme for much of the game, before Spanish defender Llera headed past Chris Kirkland with a quarter of an hour remaining.
The hosts dominated possession for long periods, but the visitors looked lively on the break and the 4,400 away fans that made the journey down the M1 had every right to feel aggrieved not to see their side collect at least a point for their endeavour.
Gary Madine had the first chance of the game for the visitors, but Lee Camp was alert to tip his 25-yard effort around the post after three minutes.
From the resulting corner the ball dropped to Jay Bothroyd in the box, but the former Cardiff striker's powerful shot was well blocked by Camp.
Forest's best opportunity of the first half came when Andy Reid played a delightful one-two with Billy Sharp on the edge of the area, but after finding himself one-on-one with Chris Kirkland the Irish midfielder hit his shot straight at the keeper.
Wednesday grew in confidence as the half went on, with Madine latching onto Michail Antonio's long throw only for Camp to snuff out the danger. Owls captain Jose Semedo then picked out Antonio with a fabulous long pass, but Danny Collins did well to scramble his dangerous cross clear.
Sharp missed two glorious opportunities in as many minutes - firing wide after Dexter Blackstock laid off Greg Halford's pass on 38 minutes and sending Chris Cohen's searching cross narrowly wide with a diving header moments later.
Wednesday's clearest opening of the half came a minute before the break, Bothroyd's corner dropping kindly for Nejc Pecnik who volleyed narrowly over from eight yards.
Bothroyd missed a glorious opportunity himself shortly before the hour mark. Full-back Daniel Jones got past Camp on the by-line and pulled the ball back for the 30-year-old, whose shot was headed off the line by Collins.
The game looked to be dwindling towards a goalless draw when out of nowhere Llera inexplicably nodded Cohen's cross from the right past Kirkland, after Sharp had failed to make contact.
Madine had a chance to equalise moments later but he headed Jermaine Johnson's cross wide, while at the other end Cohen's late effort went narrowly wide of the target.