Arsenal goalkeeper Lukasz Fabianski was inspired as he produced a string of superb saves to deny Suarez, Daniel Sturridge and Philippe Coutinho.
"I thought the best team lost. I thought the very least we deserved was a replay," added Rodgers.
"We probably should have been 2-0 up inside those first six or seven minutes. Going forward we were outstanding. I'm disappointed with the goals, the first one in particular was just a long ball into the box.
"But, apart from that, going forward we were a real a threat and are bitterly disappointed not to get something."
Rodgers added the FA Cup exit means Liverpool can "narrow" their focus to the Premier League title race.
The Reds, who have not won the title since 1989-90, are fourth in the top flight and trail leaders Chelsea by four points.
"Now we have got one competition to focus on for the rest of the season and have to really focus on these last 12 league games," added the Northern Irishman.
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