Trailing to goals from Andreas Weimann and Christian Benteke inside 36 minutes, Reds striker Daniel Sturridge pulled one back on the stroke of half-time.
The contentious penalty came just after the break when Suarez was adjudged to have been brought down by goalkeeper Brad Guzan and Steven Gerrard equalised.
"I thought we should have had a penalty in the first half when (Leandro) Bacuna handles the ball," Rodgers said.
"The second I thought was a penalty. Luis has taken it up to the keeper and, once he has touched it around him, his body makes contact with Luis.
"Obviously from Paul's (Villa manager Lambert) perspective he will think it has been harsh."
On his adventurous team selection, which saw defensive midfielder Lucas Leiva dropped to accommodate Sturridge, Rodgers added: "I go with my gut feeling. I thought it was an offensive team.
"I have played that before. If you want to blame me, blame me.
"It is a good point. I don't think we were anywhere near our level in the first half, give credit to Villa for that.
"The front two was a real threat for us and tactically we had to change it."
Villa boss Paul Lambert unsurprisingly disagreed on the penalty incident.
"Brad has pulled his arms away. It is hard for the referee to judge it. He has a split-second decision to make it but I think Brad used his experience to pull his arms away and then you get punished," he said.
Asked whether he thought Suarez had dived, he added: "I'll let you be the judge of that.
"I am not being critical of anyone. I'm not getting caught into that, the guy is a world-class player."
Of his team's performance, Lambert said: "I thought we were excellent. I thought Ron Vlaar was excellent, Benteke looked back to himself but we lost Gabby (Gabriel Agbonlahor) at a vital time and he was unplayable.
"I always thought we looked a threat on the counter-attack We might have sneaked it but I don't think anyone could begrudge us a point."
Gerrard, who played in the deeper holding role in the first half, admitted his performance - like the team's - was well below the required standard.
"They deserved a point. We were nowhere near good enough in the first half," he told Sky Sports.
"They put a lot of men around me in the first half. Whenever I got the ball they swamped me and I admit it wasn't one of my better 45 minutes.
"The problem today and the reason fans will be disappointed is our immaculate home record.
"It is no time to panic and we will carry on fighting for fourth. They are all big tests now."