Coleman, who will be expected to set City into a far higher finishing position than the 21st place they finished in last season, told the CT: "It is nice to get three new players over the line, particularly as we haven't even kicked a ball in pre-season yet.
"But we can't stop there. We still have a lot of rebuilding to do because this club wants to be in the Premier League.
"We finished fourth from bottom last season so there is a lot to do. I am hoping there will be another couple, at least, before the end of the season, and no matter where we are in the league we will be looking to do it again in the December/January window to build again.
"We don't want mediocrity from the players who are here. We don't want them to be happy with surviving in the Championship because that's not good enough for a club of this stature. We should be doing a lot better than that."
As well as signing players, Coleman still has to finalise his pre-season schedule which includes matches for the tour of Switzerland and a home friendly.