Real are top of the Primera Division and in the final of the Copa del Rey, while they have one foot in the quarter-finals of the Champions League after a stunning 6-1 victory away to Schalke in the first leg of their last 16 match.
Carlo Ancelotti's men are unbeaten since they lost 2-1 at Barcelona on October 26 - a run of 28 games in all competitions - and Casillas said: "What we've done until now is the minimum asked of us - to fight for the three competitions.
"Right now our position is privileged. We are outright leaders, in the final of the cup and - barring a miracle - in the quarter-finals of the Champions League.
"But we have to go game by game. We must think about what we have to do in March in order to get to the business end of the season in the best state possible and have it in our own hands."
Real came from behind to earn a point at city rivals and fellow title contenders Atletico last time out and Casillas said: "Never give up - Real Madrid are always characterised by that phrase. You must be at your best and not give up.
"Between all of us we have tried to cut down the distances, play better and give more attention to the defence. The result is we are now where we wanted to be seven months ago."
On his own role this season, Casillas continued: "If the boss has decided that I'm to play in the Copa and the Champions League then I want to do the best I can to help the team and play well.
"It's been going on for a few months and we aren't always going to be in this situation. Up until now the gaffer has gone with Diego (Lopez) in the league and he is playing very well.
"We are leaders on our own merit and a lot of that is down to Diego.
"I don't feel undervalued. When I'm out and about I always receive warm messages - and you have to feel valued by yourself."
Sunday's opponents Levante are unbeaten in five games since the 5-1 mauling at Barcelona on January 29.
Currently eighth in the table, they retain hopes of European action next season, with the 2-0 midweek defeat of Osasuna leaving them a comfortable 13 points clear of the bottom three.