The home side were 3-0 down inside 20 minutes when former Liverpool forward Aspas converted a penalty. Theo Bongonda doubled the lead before Daniel Wass scored the third.
The team was whistled off the pitch at half time with fans in the half empty stadium turning on Lim and Sporting Director Jesus Garcia Pitarch.
Valencia’s president Lay Hoon Chan was in the directors’ box at Mestalla to hear the jeers. She had returned to Spain from Singapore after Cesare Prandelli quit on December 30, leaving the club 17th in the table on 12 points after 15 games.
Club delegate Voro Gonzalez stepped in as caretaker boss for the fifth time in recent years as the club look for their 10th coach since they sacked Unai Emery in June 2012.
Valencia keeper Jaume Domenech said:
‘The game was a disaster. I don’t think we deserved to be 3-0 down in the first half but all we can do is keep working and try to treat the second leg like a final.’
But caretaker boss Voro said the tie was ‘almost impossible to turn around.’ Dani Parejo pulled a goal back for Valencia but John Guidetti made it 4-1 on 75 minutes.