Demba Ba capitalized on Steven Gerrard's slip on the stroke of halftime to give the visiting side the lead, while Fernando Torres raced through to set up Willian for an easy second late on to seal a famous victory.
Much of the match was defined by Liverpool's inability to break through Chelsea's massed defensive ranks, and afterwards Rodgers poured scorn on Mourinho's approach.
"We just couldn't find the breakthrough - there were probably two buses parked today, never mind one," he told reporters.
"Jose has got his result today, credit to [Chelsea]. Its the opposite of how we want to play. It's not difficult to coach, 10 players in the 18-yard box."
Mourinho, however, remained bullish about his team's performance, insisting the club deserved to win and challenging the assertion that his tactics were defensive.
"The best team won," he told reporters. "The team that deserved to win won.
"Defensive display? I am confused what the media thinks about defensive displays. When a team defends well you call it defensive."
The Chelsea boss also brushed off criticism that his team looked to waste time and break up Liverpool's attacking rhythm throughout the game.
"Time wasting? What is that?," he added. "We never spoke about this when we played lots of matches this season. Now we're speaking about it."