Missing out on his prime target Dempsey, with the Americans not willing to go above £4m, will not change his view of Liverpool, which he hopes will be his home for "many years to come".
Rodgers said: "I love it here. It's a way of life for the people. It's just the culture of the city, the people and the club.
"It's a hand-in-glove fit really. I wasn't going to leave Swansea for anyone. I was quite happy to be at Swansea for the next ten years.
"I loved the city, the supporters. It had to be a unique opportunity for me to leave. To come here to one of the best clubs in the world, despite the difficulties, was something I really wanted to have a go at.
"Some clubs can be a gateway for you in your career. This is a club I hope to be a final destination."