The club's crippling debts forced them to sell World Cup winners David Villa and David Silva last year and experienced stalwarts like Carlos Marchena and Ruben Baraja also left to be replaced by low-profile new recruits.
Defying expectations, the 39-year-old Emery has steered Valencia into third place in La Liga and came close to putting out Schalke on Wednesday. They took the lead on the night to go 2-1 up in the tie before losing 3-1.
An ability to score late goals which has served them so well in the league deserted Valencia in Gelsenkirchen, however, and as they pushed for the second away goal that would have put them through Jefferson Farfan sealed victory for Schalke with a late strike.
"It was the game we had prepared," Emery, well-known for his meticulous preparation for matches, told reporters.
"Other times we haven't deserved to win and we did, but today we lost in a game in which we just lacked a little luck.
"We played the way we wanted to and we had various chances to make it 2-2. It's tough, we are massively disappointed."
Out of Europe and the King's Cup, Valencia only have the league to play for but they are the best of the rest in Spain as Real Madrid and Barcelona tussle for the title.
They are 13 points adrift of Real and four ahead of fourth-placed Villarreal in the last remaining automatic qualification slot for next season's Champions League, with 11 games left to play.
Fans who look back with fondness on Rafa Benitez's era when he won a league and UEFA Cup double in 2004 have often shown impatience with Emery during his two-and-a-half year tenure.
Unconditional support has hardly been forthcoming from the board either, though club president Manuel Llorente went a step further than usual when asked about his coach.
"It's been very tough because we had high hopes we would progress. We spoke to the players and the coach to try and cheer them up," he told reporters after visiting the dressing room.
"At the moment, we aren't thinking of any other coaches other than the one we already have. We continue in third place and we want to finish third."
Missing out on a quarter-final payday is painful for Valencia, but a return to the Champions League next season is vital to the club's long-term stability and, probably, Emery's future.
"Direct qualification for the Champions League is the club's objective," Spain winger Juan Mata told reporters.
