Liverpool manager Brendan Rodgers is still keen to add to his six summer signings already but he will have to wait to begin work with one of his new arrivals.
Defender Dejan Lovren, signed from Southampton last week, will not join the club on the latter stages of their pre-season tour in America.
The Croatia centre-back, who completed his move on Sunday, will remain on Merseyside as he does not have the necessary travel documents.
"Unfortunately he can't come out here because I don't think he has got his visa to travel out, so he is working back at Melwood with the staff and he will be ready to join us whenever we get back," said Rodgers.
Further defensive reinforcements are expected with the Reds boss still chasing a left-back and there is room for another striker after a deal for QPR's Loic Remy collapsed.
Forward Rickie Lambert and midfielder Adam Lallana have also been acquired from Southampton, while Benfica winger Lazar Markovic provides more attacking options and Bayer Leverkusen's Emre Can has added depth to the midfield.
However, with Divock Origi loaned back to Lille for a year Liverpool still look light up front following the departure of Suarez.
"We still have some positions that we want to fill within the squad so that by the end of August we have a strong group of players to go forward with. We've still got some business to do," added Rodgers after the City victory.
"We've brought in specific players for specific roles, players that have the profile of how we work.
"A lot of the players that have come in, the transition has been very smooth and that should make the adjustment that bit easier.
"Of course some of them are young and coming to a different country, like Emre Can. That will take a little bit of time.
"The players are transitioning very well, though it will take a little bit of time."