Grant said: "Since we beat Valencia (in October), we have won a lot of games and we have played better football - even with a lot of injuries.
"It shows the character of the team. You see Arsenal when they have injuries and what has happened to them in the last couple of games.
Grant's surprising attack is the first time he has stepped out of the comfort zone since he replaced Mourinho, but he is clearly increasing in confidence.
Chelsea qualified for the second round of the Champions League with a game to spare after their 4-0 win in Rosenborg at the end of last month. They are three points behind Arsenal in the Barclays Premier League.
Grant has had to contend with injuries to key personnel - including Didier Drogba, Petr Cech, John Terry, Ashley Cole, Ricardo Carvalho and Frank Lampard - but they are still in the hunt for four major trophies.
The Chelsea chief added: "We have a big squad, but other clubs have big squads. We have used ours in the best interests of the club.
"We have had a lot of injuries in a very short space of time, but the players have done what we needed them to do.
"They have done everything we have asked of them. Carlo Cudicini, Andriy Shevchenko, the defenders and the midfielders have all come in and shown their quality. You can't ask for more than that."