The Blues took the lead at Stamford Bridge through a first-half goal from Cesar Azpilicueta, only for Javier Hernandez to find a way through in the final quarter of the match to see the spoils shared.
A week on from throwing away all three points from a winning position against Tottenham Hotspur, Rudiger acknowledges that lessons must be learnt if his side are to have any hope of making up the 10-point deficit on Spurs in fourth place.
"I think we begged for the goal, and in the second half, or even in the first half we could have finished the game, but like the last few months we couldn't, and we conceded at the end," he told Sky Sports News.
"It's not easy to explain. I don't understand after we go 1-0 up why we always drop off and let our opponents come onto us. We could have done better, of course - we gave them a gift, it was the first clear chance they had and they scored.
"The thing is we have to start playing good football and winning games, because if we don't do that we cannot get in the top four."
Chelsea have lost five, drawn three and won three of their 11 league games since the turn of the year.