Morata has scored six League goals in as many matches – including his hat-trick against Stoke – since joining from Real Madrid for a club record £58million.
Cahill said: “It’s great that, after Diego, we have another striker coming in and scoring straight away.
“I’m sure Alvaro wasn’t surprised by the pressure. He knew that it would be there when he joined and he came from a huge club anyway.
“Being a striker for Chelsea comes with a lot of pressure, but he has played with big players and big teams. He knows how to handle that and I don’t think it has been an issue at all.
“A few familiar faces helps and there are obviously a few Spaniards that Morata knows here. He is a fantastic guy, down to earth. His personality makes it very easy to get on with him.
“You can see from his performances that he is enjoying life at Chelsea. For us, it’s about having his back and making sure we provide for him. The lads up front did that at Stoke. He finished all his chances off and his confidence is flying.”