The Reds' sole focus is now on the Barclays Premier League as, a week after beating Arsenal 5-1 at Anfield, they fell out of the FA Cup as Alex Oxlade-Chamberlain and Lukas Podolski netted for the Gunners to set up a home quarter-final with Everton.
Steven Gerrard converted a penalty after Podolski tripped Suarez and a further trip on the Uruguayan, this time by Oxlade-Chamberlain, went unpunished - much to the bemusement of Rodgers, who does not feel his striker's reputation for going to ground easily should have impacted on referee Howard Webb's decision-making.
"He's always asking questions of defenders, and quite a lot of the time he doesn't get what he deserves," Rodgers said.
"The one at Chelsea (when Samuel Eto'o fouled Suarez in December) was a clear penalty. He's got a penalty but should've deservedly had two penalties today.
"And if it is a penalty he should have it, irrespective of what his reputation is.
"I thought that was quite an easy decision for the ref.
"Luis has a touch, gets around him and it looks a blatant penalty.
"We're bitterly disappointed to have not got that because then it just keeps our momentum going for the final stages of the game."
Arsenal boss Arsene Wenger tried to sign Suarez in the summer, but believes the striker is prone to exaggerating.
"I rate Suarez as a player," Wenger said. "If we had him in the team we'd have a few more free-kicks.
"But it's always difficult to know with him: was it really genuine contact?
"It was contact, I don't deny that, but he's very good to make more of it every time."
Rodgers did not speak to Webb immediately after the game, but will ask for an explanation.
The Liverpool boss added: "For me, it's gone. You can't change it, you can't affect it. I'll speak to an assessor.
"It would be nice to know why it wasn't given, because it can be a defining moment in the game."
Gerrard might have been sent off in the second half for tripping Oxlade-Chamberlain after being booked for an earlier foul on the winger.
Rodgers added: "I think it was a foul. I'm not so sure it was a yellow card. Howard's used his commonsense. He got that correct."
Arsenal's triumph vindicated Wenger's decision to make seven changes, the majority of which came about for "medical reasons".
Lukasz Fabianski was given an opportunity in goal, while Jack Wilshere (stiff back), Santi Cazorla (ill), Kieran Gibbs (muscular problem), Bacary Sagna (tired) and Olivier Giroud (tired) were either on the bench or not involved.
Wenger insisted Giroud was not dropped for personal reasons following an alleged affair.
"He has made a statement," the Gunners boss said. "We'll deal with it internally. I want to respect his privacy."
It was a welcome victory for Arsenal after a trying week following the mauling on Merseyside and ahead of Wednesday's Champions League last-16 first leg against European champions Bayern Munich.
"It was vital for us to respond to the disappointing performance we had against Liverpool last week," Wenger added.
"I'm very pleased with the intensity of our commitment, our response, our determination.
"You could feel there was a clinical desire in my team to take every opportunity to kill them.
"It was a great game between two great teams. It was a fantastic FA Cup tie.
"Many people questioned the FA Cup but today it delivered a great football performance."
Wenger might have been excused a feeling of deja vu early on as it appeared Liverpool would accelerate into an early lead.
Daniel Sturridge twice had opportunities in the opening five minutes to fire Liverpool into an early lead but saw his run of scoring in eight successive games end.
"He's disappointed and he'll be disappointed for the team as well," Rodgers added.
"I thought our performance level was outstanding.
"To come here, virtually dominate most of the game and look a real threat going forward, to end up with nothing in the game disappoints because it was a competition we wanted to do well in.
"We could very easily have had another five or six goals today, but we weren't as clinical."
Liverpool are four points behind Premier League leaders Chelsea and now have one target.
Rodgers added: "It narrows our focus now into one competition and we just continue with the confidence and the belief we've been playing with.
"We're going to have a really exciting 12 games to finish."