The Columbian forward managed a measly four goals in 29 appearances following his loan spell from French side Monaco.
However, speaking to the media ahead of the Community Shield on Sunday, Mourinho expressed his delight at how the players first week at the club had gone.
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As quoted by the FA, the Portuguese manager said: "I am very happy with his first week, and it’s only a week, but I'm happy. As a start I'm just worried that he adapts and he is happy and we are happy with him, he performs and he gives us what we want.
“I think to become a ‘super scorer’ again – let’s see what happens. I was not expecting him to come here and play 20 minutes against Barcelona and score three goals. I was not waiting for that. I was waiting for his determination to work as part of the team, understand the way we play football and I'm happy.”
Mourinho said he is a big admirer of Falcao, and is expecting the striker to contribute to the side in more ways than just goals. The Chelsea boss is hoping to use the Columbian's strength and ability to hold up the ball and allow other members of the side to get into goalscoring positions.
Diego Costa is likely to be the Blues' starting striker for the season ahead after his tally of 20 league goals in 26 appearances, however the manager has said whatever striker he decides to play should be feared by the opposition.
“We have three top strikers, if one is injured we have two. No concerns or no protections, it’s a position we are very strong. We have a fantastic group of strikers."
Along with Costa and Falcao, Chelsea can also call upon the services of Loic Remy, who scored seven goals despite starting just 19 games.
Mourinho also confirmed that Costa is fit for selection in the Community Shield on Sunday and even hinted that he may play two up front, like he did on occasions during some of the pre-season games.
Will Falcao be a success at Chelsea? Who would you start in the Community Shield? Have your say below!