The Israeli led the Blues to their first-ever Champions League final, where they lost to Manchester United on penalties, but Mourinho claimed he would have gone one better had he stayed at Stamford Bridge.
Grant is confused by the Inter Milan coach's unprovoked criticism and has defended his efforts in resurrecting a Blues side that were in turmoil when he took over.
He told the News of the World, “What the fans need to remember is that Jose did not leave me a team that were champions, that was Manchester United and we were in sixth position after a very poor start to the season.
“Everyone was in shock. The atmosphere in the dressing room was not good, critics were saying the football was boring and negative and we had just had a poor draw with Rosenborg in the Champions League.
“The supporters were booing the team after that match, the stadium was half empty and Jose knew his time was up.
“He then walked out a couple of days before an away match with United when Didier Drogba, Frank Lampard and Ricardo Carvalho were all out injured and I agreed to step in.
“I was director of football and was enjoying my job. Jose agreed I should come and we worked for three months together. He did his job and I tried to help him. I felt it was a very important role. But things were not good. Morale was low and questions were being asked.
“With a lot of effort — and a lot of thinking and hard work — I started putting the team back together again.”
What's Stopping Mou?
Grant then launched a stinging counter-attack at Mourinho, insisting the Portuguese had plenty of chances to lead Chelsea to European glory.
“I don’t see how Jose can claim he would have won the Champions League if he’d still been in charge,” the 53-year-old continued.
“He was boss for more than three years and he didn’t even make the Champions League final once. What stopped him? He had the biggest budget in the history of football, some of the best players and an owner that gave him everything.
“But he got beaten twice in the semi-finals by teams with half the budget he had at his disposal.
“What he forgets is that we beat Liverpool with a team that had (Fernando) Torres in and only missed winning the biggest prize in football by inches — and that penalty shoot-out miss did not make us a bad side.”
One Of The Best
Nicolas Anelka's flubbed spot-kick doomed Chelsea to trophyless season and signalled the end of Grant's whirlwind spell in the Stamford Bridge hot-seat.
But people often forget that the Pensioners came agonisingly close to claiming a double last term, as they battled Man United right to the wire for the Premier League title - a remarkable achievement after the start they endured.
And Grant said, “Jose says that I did ‘nothing’ in the League. Perhaps his memory is failing him because my winning ratio of games was second to none. We won all the big games at home when I was in charge, beating Arsenal, United and Liverpool.
“I am told one of the best in their history. We won all the big games at home when I was in charge.
“If we hadn’t started the season so badly under Jose, we would have been champions — it’s a fact — but the dropped points cost us dearly at the end. We paid the price for a poor start under his guidance.”
Mike Maguire, Goal.com