A late flurry of United goals heaped the misery on the Welsh club at the end of a week which has seen them one of their finest-ever players, Gylfi Sigurdsson, depart for Everton.
Without the Icelandic playmaker's craft and guile, Swansea struggled to create. They are also still missing last season's top-scorer Fernando Llorente, who is still injured, and Clement admitted that he needs to sign players.
“We absolutely need more quality players to come in, so we have a chance of being competitive this year,” Clement said.
“The sooner we can do it the better. It could go later in the window but the necessity is there. It’s clear.
“We were competitive for long periods of the game. Up until the second goal the difference was a set-play and generally, the shape was good.
“I made some offensive changes because I don’t want to be a coach happy to lose 1-0 at home, but we ended up playing to their strengths and they punished us.”
“Today I’m more disappointed with the result than some of things I’ve seen. I was happy with some of the things defensively, not so happy offensively.
“We went a goal down and tried to do something about it but we got punished and it’s hard to take.”
Next up for Swansea is an EFL Cup tie against MK Dons before travelling to Selhurst Park next week to face Crystal Palace, who have opened their season with two straight defeats.