Moffat previously criticised CBS for producing its own Sherlock Holmes series after being denied the opportunity to remake his BBC show Sherlock, calling the network's behaviour "pretty remarkable".
"I think [the people who make Sherlock are] okay with it now," Liu told Vulture. "I think they were shown the [Elementary] pilot and they saw how different it was from theirs.
"I don't know for sure but I thought that the creator from the original Sherlock had seen the pilot and he said that he was really impressed and pleased with how it turned out, and he saw that the correlation was completely different."
The actress - who plays Watson to Jonny Lee Miller's Holmes - compared starring in Elementary to her experience on the Charlie's Angels movie series.
"Sometimes when there's a remake involved... people are kind of scratching their heads like, 'Why are you doing that? It's going to be so ridiculous'," she admitted. "And you never know how it's going to turn out, but I think we all have faith in it and we hope that it's received well."
Elementary debuted last night in the US and will air on Sky Living in the UK from October.
> Cumberbatch denies Sherlock, Elementary feud: 'There's no fight'
> Elementary exec on romance: 'It's not what the show was built to do'
Watch a clip from Elementary below: