
Grant, who took over from Jose Mourinho in September, has seen his side lose in the final of the Carling Cup and then on Saturday be knocked out in the quarter-finals of the FA Cup at the hands of Championship side Barnsley.
Chelsea are through to the quarter-finals of the Champions League and also have a chance in the Premier League, sitting in third, eight points behind leaders Arsenal, but with two games in hand.
But Grant has come under fire for his side's failure to beat any of Arsenal, Manchester United or Liverpool.
And when asked if he believed his job is at risk should Chelsea fail to win a trophy, he said: "I will accept it.
"When I am responsible for the team, and when my team loses at Barnsley, there will be many negative things said about it.
"On the other hand, we have two major competitions left. I am concentrating on them, not other things. But this is a massive disappointment."