The away side were the dominant force for the majority of the tie but failed to find the required quality in the final third to overturn the two-goal lead which Spurs built up inside 16 minutes.
But Rodgers believes his side "never got the rub of the green" from Dowd, pointing to the "assault" on Steven Gerrard by Mousa Dembele and insisting that Clint Dempsey "dived" to win the free kick which led to Tottenham's second strike.
"We never got the rub of the green," the Reds boss told Sky Sports News. "It was a little embarrassing.
"[We had] two clear penalties. [Dembele] on Steven Gerrard was bordering on assault, never mind a tackle. It was frightening how we got never the penalty for that. Then Luis Suarez got kicked by William Gallas.
|12/1||Luis Suarez is 12/1 with William Hill to score a hat-trick in Liverpool v Southampton|
The Northern Irishman added in the post-match press conference afterwards: "They say it evens itself out over the season, so if that's true we're going to get a hell of a lot of decisions in the second half of the season.
"I thought we were absolutely magnificent tonight," Rodgers added. "I don't think we can come here and play any better. We would have been disappointed if we drew the game but to have actually lost it is bitterly disappointing. [The players] were absolutely fantastic.
"We started reasonably well in the game with the ball but we found ourselves 2-0 behind very quickly in the game and that can be difficult but the reaction of the team for the rest of the game was relentless. Our overall play was outstanding but we were unfortunate we couldn't at least get the draw."