A mistake by Steven Gerrard let Demba Ba in for the opener in added time at the end of the first half, and with seconds remaining substitute Willian added a second goal on the break.
The visitors successfully resisted Liverpool's attacking flair, with Mourinho's side employing every trick in the book to slow down play, and it more than paid off as the usually free-scoring Reds ran out of ideas.
Mourinho was unrepentant about the match plan that led Liverpool manager Rodgers to say: "I think there were two buses parked today, never mind one."
An under-strength Chelsea side mounted a defensive exercise that brought rich rewards, and Rodgers added on Sky Sports: "It was like a back six with three midfield players in front of that. That's 10, with the goalkeeper, for 90 minutes consistently behind the ball.
"Unless you get that early goal, it doesn't entice them to come out. It was clear that they'd come certainly not wanting to win the game, with the time-wasting and whatnot.
"The players gave everything and we couldn't quite get that wee bit of luck."
Drawn further on Chelsea, Rodgers added in his press conference: "They have a different style to us but if it gets results, great. Jose will be happy with that.
"Congratulations to Chelsea as they won the game, although they came for a draw.
"It is totally opposite to how we want to play but give credit to them for winning the game.
"It is not difficult to coach, putting 10 players on the edge of the 18-yard box.
"They got booked for time-wasting in the 92nd minute but I think everyone could see from the first whistle that was their plan - to frustrate."
Rodgers attached no blame to Gerrard for the error which proved so pivotal.
"Steven is a boy who has picked up this club so many times and it was just really unfortunate because he slipped at a crucial moment and it was right on half-time," Rodgers said.
"He was doing everything he possibly could and we hoped there would be one or two who would step up to the plate instead of him, but we couldn't quite do that.
"There's certainly no blame because we are in the position we are in now because of him; he's been instrumental for us this season.
"It's just unfortunate that he's slipped over. It could have happened to anyone. This is a guy that is so strong mentally.
"He probably got frustrated but I thought he showed his courage because after that he still kept getting on the football, he still tried to pass; at times, he broke through and broke the line to get in.
"But he and our other attacking threats just couldn't quite make the breakthrough. Give credit to Chelsea for that; they sat in really deep."
City are favourites for the title now but Rodgers is confident his side can bounce back from the end of an 11-match winning run and finish the season on a high.
"City will now feel they can go on and win their games," Rodgers said. "We'll just recover now, we'll focus on the next game and continue with that positive mentality that we've had throughout the season - because that's the reason why we are where we are."
Liverpool go to Crystal Palace on Monday, May 5, before finishing off at home to Newcastle six days later.
Chelsea's win moved them two points behind Liverpool at the top of the table. City, with a match in hand, stand just a point further back after their win at Crystal Palace, and have the superior goal difference of the three sides chasing the trophy.
Mourinho had no doubt Chelsea earned their reward at Anfield.
"The best team won, in my opinion," said Mourinho.
"The team played brilliantly. Every player was magnificent. No mistakes. I think it was a fantastic performance by my players.
"I am not looking for credit. I am very happy with my players, they know how pleased I am with their work and that is what they need from me.
"Time-wasting. What's that? You never spoke about this when we played lot of matches this season."
It appears the title race will go down to the wire but Mourinho does not consider his team to be contenders.
"There is no chance. We were waiting for this match to be the title match (decider) for a long time but for some reason this match didn't become the title match," he added.
"It was three important points and we need one more to finish third and if we finish third we are in the Champions League automatically.
"A champion is only one team so we don't want a trophy to finish third but we can say we won both matches against the champion as we won both against Liverpool and against City."
Mourinho, who revealed captain John Terry has a chance of being fit for Wednesday's Champions League semi-final second leg against Atletico Madrid, had sympathy for Gerrard.
"Nobody enjoys it when someone makes a big mistake," Mourinho added.
"I prefer to say Demba Ba was fantastic in front of the goalkeeper."