A stunning free kick from Gareth Bale followed up Aaron Lennon's first half tap-in, with Bale turning the ball into his own net to pull a goal back for Rodgers' side.
But the Liverpool manager was incensed at Dowd for turning down two penalty claims - 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 tonight 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," Rodgers said after the match.
"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..."
Bale tore West Ham apart at White Hart Lane on Sunday and he began this evening's game in similarly devastating fashion, embarking on a 50-yard run before playing in Lennon for the opener after seven minutes.
The Welshman then powered home a brilliant swirling free kick to make it 2-0 after 16 minutes, the ball looping and dipping over the wall leaving Pepe Reina completely nonplussed.
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.
Liverpool tried to levee the score, 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."
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," said the Tottenham manager.
"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."
The result moves Tottenham above Arsenal and Everton to fifth, and just three points off third ahead of Saturday's match 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."
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