Others like Didier Drogba, Frank Lampard and Ricardo Carvalho, regular first-team players, may identify the near misses of this season as the moment to move on. Why? Because Grant has yet to demonstrate that he can do what Mourinho did and win the big prizes on the big occasions.
Grant's prospects of continuing his job into next season would have been greatly enhanced had his team won last night, but he was still deeply impressed by the effort of his team in pouring rain on a pitch of questionable quality.
"It's hard to lose on penalties," he said. "I thought we dominated the game after the first 30 minutes. I'm very proud of what we did and the way we played.
"We showed great spirit and our quality was good. I think my players can look back and be proud of what they achieved this season."
Grant should take satisfaction, too, from the role he has played. He may have finished the season without a trophy but succeeding Mourinho was always going to be a formidable challenge.
Sir Alex Ferguson, jubilant at repeating his European triumph of 1999, still found time at the end of a dramatic evening to give Grant his support.
"Avram was thrust into the job at a difficult time," he said. "But in terms of consistency of results I think he's the equal of Mourinho."
However, is Grant really the man to convert Chelsea into something more than just a team of power and efficiency?
They lack the kind of style that lifts Manchester United and Arsenal above the ordinary. There were one or two moments in an unimpressive match when United reached breathtaking heights with the quality of their passing and movement.
For instance, in the build-up to Cristiano Ronaldo's well-directed back post header from Wes Brown's cross which gave them the lead in the 26th minute. Frank Lampard, Chelsea's most influential player, equalised when a shot from Michael Essien bounced off two United defenders and fell into his path.
But, by the time Didier Drogba struck a shot against a post in the 77th minute, it was beginning to look as though both teams had settled for extra-time.
Lampard nearly sealed it for Chelsea when he hit the bar in the extra period but fatigue and frustration then set in.
Tempers frayed in the final nine minutes when referee Lubos Michel booked four players and sent off Drogba for slapping Nemanja Vidic.
It was a development that Drogba - and Chelsea - would regret when the time came to decide the match on penalties. Ronaldo was the only player to have had his spot-kick saved before John Terry hit the post with Chelsea's fifth.
Had Drogba been on the pitch, the Chelsea captain would not have been asked to take one of the first five penalties.
Anderson then scored for United, Salomon Kalou for Chelsea and Ryan Giggs for United. Then Edwin van der Sar saved Nicolas Anelka's weak shot and secured the trophy for United.
"Fate played a hand because that slip by John Terry gave us an opening," said Ferguson, referring to the 50th anniversary of the Munich air disaster.
"We had a cause which was very important. People with causes are difficult to battle against. I feel very, very proud."