The defeat means Fulham have now lost a record 11 consecutive London derbies in the top flight.
Castagne opened the scoring with a 56th minute header and Vardy scored in the 74th and 84th minutes with both goals coming from the penalty spot - the first after he had been pulled back in the West Brom area.
"Before that, we had a situation with a spit from Di Maria," the Portuguese coach added.
It was the debut for Bratislava's new coach Darko Milanic who just signed with the team on Monday.
Garcia will be expected to get results but with a squad that looks much weaker than last season that looks difficult; what the former Watford boss desperately needs is a positive start in Sunday's derby at home to Levante.
18-year-olds Kays Ruiz-Atil and Arnaud Kalimuendo made their first team debuts in attack while between the posts was 20-year-old Marcin Bulka, who was making just his second appearance.
However, Villas-Boas didn't think Alvaro - who earlier accused Angel Di Maria of spitting at him - would have committed such a wrongdoing.
Seven-time Serie A champions Corinthians, meanwhile, are 15th with just two wins from nine matches so far.
Before the game, PSG hadn't lost in Lens since 2009, and hadn't lost the opening game of a Ligue 1 season since 2011.
Chongqing pocketed two wins consecutively to rank six in the league, only two points clear of Hebei in the Suzhou division.
Florenzi started his football career in Roma's youth teams and turned pro in 2011. He spent almost all his career at the Serie A side where he scored 28 goals and provided 32 assists in 280 appearances.