Goals from Didier Drogba and Alex settled the match for the visitors and Grant insisted that winning in style would be his main aim during his time at Stamford Bridge.
Asked if he has an obligation to entertain, he said: "Yes. I have an obligation for this. This is the right way in modern football, there is no other way.
"Of course, you need to win games, but the way to the winning is also important, not like it was before."
He said: "I want to look forward. As you know, I have full respect for the past here. I am looking only for the positives from the past.
"We are trying from this base to change a little bit, even more than a little bit, and do it my way.
"We will do it my way, but I will not even say one negative word about the past because I don't have negatives to say about it."
If Grant left Teesside a happy man, opposite number Gareth Southgate was left to reflect upon a third successive Premier League defeat.
He said: "It was, by the end, very flat, which when it is at home, is always disappointing - well, more than disappointing.
"We didn't get out of the blocks at all, we didn't make contact with them up to the point where they scored the goal, really.
"That's the fourth game on the bounce where we have conceded in the first 10 minutes, and it gives you an absolute mountain to climb."