Leicester are in crisis having lost their last five top-flight matches to drop to within one point of the relegation zone.
Saturday's fixture against third-tier opponents could give them some respite, but Ranieri feels the Foxes should not be expected to come out on top.
"They have beaten two Premier League teams," under-pressure Ranieri said at his pre-match media conference.
"We know this. We are the underdogs if they beat Bournemouth and Watford, who are above us in the league.
"Millwall are a good team - compact and full of confidence. They play well together but we are ready.
"We have to play for our fans. There will be 3,000 of them there with us to support us and I want to see our players fight.
"My mind doesn't change if I win or if I lose. I stay positive to try to help my players. You have to continue to believe.
"We are working so hard. When you work hard, when you believe in something, at the end you achieve something."
Ranieri is planning to make major changes to his line-up like he did in the previous round against Derby County, with Premier League survival his top priority.
The Leicester manager may be short of attacking options, though, with Islam Slimani ruled out and Leonardo Ulloa a doubt.
Ranieri continued: "Our target is the Premier League - that is it.
"We want to do our best but the goal is the Premier League and we want to be safe at the end.
"I want to give another opportunity to the players who played against Derby. Slimani is not ready yet. He feels something in his groin and is not available.
"Ulloa started to train but not properly because he feels something. He didn't finish the session on Thursday so we will have to wait."