New manager Arne Slot is yet to bring in his first signing at Liverpool.
After victory at Ipswich, Robertson said: "I think we have an unbelievably strong squad.
"You look at the bench today and even the lads who maybe didn't travel, we have a fantastic squad and the quality was shown a lot in the second half today.
"Certain positions are spoken about and things like that but I thought people were really good and stepped up to the plate. We have a lot of quality in every position and if that is the squad that we go forward with then I believe that is good enough to compete in the competitions we want to compete in.
"Everyone wants new signings - fans want new signings, people want new faces around the building - but I think the squad we have got just now is incredibly strong and if we don't make any signings, we're in a good shape to crack on for the rest of the season."
Robertson added "We've been in the game long enough now that we know people want you replaced and people want new signings. People want younger faces after seeing a good 15 minutes in one game or whatever - that's the way football is.
"That's the industry that we're in. We just try and block that out. We know the quality that we have got and it is about showing that on a weekly basis. If you don't show that, of course the club would look to replace and people would put more pressure on it.
"It's up to us to perform on the pitch and I think so far, so good in pre-season and today but it is up to us to show that over a longer period of time. If we do that, we'll hopefully show everybody the quality that we have got."