In an interview with Sky Sports News, Thompson pointed out that a lack of defensive signings in the summer transfer window left Liverpool without the quality and depth at the back to compete for the Premier League title.
The Liverpool legend said: "I still think we could have strengthened, without a doubt. We did sign Andrew Robertson, but he didn't play against City or Arsenal, so yes we should have signed somebody.
"But for me, the selection was the big issue. After such an impressive result there is no reason to make changes because it's such an important thing for a defence being settled, especially against such an offensive team when you've got to trust your teammates."
Liverpool were favourites to sign Southampton defender Virgil van Dijk in the summer, but Jurgen Klopp's side were unable to get a deal through despite a lengthy pursuit.
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