Does anyone remember the last time Villarreal lost three consecutive matches in the league in a single season? You might guess it happened in the dreadful 2011-12 season, and you'd be right. They were in fact the last three matches of José Molina's reign, two of which were lost with virtually the last kick of the match: a 2-1 loss at Zaragoza and a 1-0 loss at Levante. The match in the middle was a home loss against Getafe, 2-1.
Other than that, you have to go back to September 2009, when Ernesto Valverde's time in charge included three losses in eight days, to Athletic Club, Real Madrid and Deportivo; December 2008, though this one was a scheduling nightmare--the Submarine went down to Sevilla, Barcelona, and Real Madrid, in that order. (And after those three losses, our next match was drawn 3-3 against Valencia!).
Finally, in the 2006-07 season (where we finished fifth) we had a strange bout of impotence in February; we lost to Deportivo 2-0 at home, and to Zaragoza 1-0 on the road. But the first of these losses was on February 4, 2007 to Recreativo Huelva, to whom we had sold Santi Cazorla (we had sold him with a buyback agreement, so it was technically not a loan, but close to it).
Huelva won 2-1; Cazorla was in the starting lineup, and there were three current Villarreal players (well, one currently on loan) who played in that match. Cani started but was replaced at halftime; Jony Pereira came on as a substitute (for Diego Forlán) for Villarreal, and Ike Uche came on as a sub for Huelva. Two other Villarreal connections, too: the first goal was scored by none other than Juanma, who played for us a bit in 2012-13; and the coach of Huelva that day?
Of course, Marcelino!