Fellaini has admitted that the draw was not the ideal result for United and believes that they must improve before facing the Blues on Sunday.
"I don't think it was a good result for us because the next two games will be difficult," BBC Sport quotes him as saying. "The manager asked me to put pressure on the box and to keep fighting. I did and I managed to score.
"In the second half, the style was more aggressive and we looked better. I have waited a long time to score my first goal and I hope to score more goals for Manchester United.
"We offered too much space in defence but next week is a big game and we have to learn to focus for the whole game. We know we have a problem with the balance between defence and attack but we play and train all day to get better. It is a big game for us [against Chelsea] and we have to win. I am determined to get things right - that's why we play football."
Tonight's result means that United are still looking for their first away win of the season.