Spurs ran out 2-1 winners at White Hart Lane thanks to a stunning free-kick from Gareth Bale and Aaron Lennon's first half tap-in.
Rodgers, whose team pulled a goal back courtesy of a Bale own goal, was infuriated at Dowd for not awarding them two spot-kicks - one for a foul on Steven Gerrard by Mousa Dembele, and the other when William Gallas took out Luis Suarez in the dying minutes.
Earlier this season, Rodgers complained that his team were not getting enough decisions from officials, and he was deeply unhappy on Wednesday that Dowd awarded the free-kick that led to Bale's goal when Clint Dempsey went down under the slightest of touches from Jordan Henderson.
"Nothing is going for us away from home, that's how its been all season in terms of decisions," Liverpool boss Rodgers said in his post-match press conference.
"Clint Dempsey has been clever (with the free-kick). He gets a hand in his back and goes down.
"We should have had two [penalties tonight]. It's incredible to have gone through the season without getting a penalty.
"The Steven Gerrard one was nearly assault. How is that not a penalty?
"Watch the second one. Luis Suarez spins, William Gallas swings his left foot, catches him and he goes down.
"The statistics will tell you that we've been in the box as much as anyone, but to arrive at this stage of season and not get a penalty..."
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Tottenham were left desperately hanging on pretty much from the moment that Bale's free-kick doubled the hosts' advantage, with Suarez and Henderson both guilty of missing good chances.
"We will struggle to play as well as that and not get anything," Rodgers added.
"We were absolutely outstanding. We would have been disappointed had we come away from that game with a point."
In the end it was Bale's masterclass performance that proved to be the difference between the two sides.
The Welshman eased past four Liverpool players on a 50-yard run before squaring to Lennon for Tottenham's opener and his 30-yard swirling free-kick was a strike Cristiano Ronaldo would have been proud of.
The only negative for the former Southampton winger came with his comedy own-goal in the second half when he found himself in the way of Lennon's goal-line clearance and saw the ball rebound in off his head.
Bale has now scored 10 goals for club and country this season - and Villas-Boas admits the biggest teams on the planet will have been alerted by the winger's form.
"Tottenham as a club want to keep him here as long as we can but we understand players like this have propositions, have market which is the nature of the game," the Spurs boss said.
"At the moment he's doing extremely well for Spurs and we are absolutely amazed with what he can do for us. Hopefully, we have no doubt he can become a top player in the future. He is on to a great career."
Reina was powerless to stop the ball as it dipped and swerved in to the net for Tottenham's first and Bale nearly beat the Liverpool stopper twice more from similar range.
"Ronaldo showed you can almost hit the ball from the bottom to the top and it has an effect it changes direction," Villas-Boas said.
"Gareth has the power to hit the ball at that pace and that's why the ball gets so many effects."
Spurs climbed above Arsenal and Everton in to fifth tonight and are now just three points off third going in to Saturday's game against Fulham.
"This is an important result given this is a midweek fixture when most of the teams have dropped points and we have gained some," Villas-Boas said.
"It puts us in a really good position. If we can sustain this momentum in our next three games we can maybe join the top where we want to be."