The revamped trade deal for North American economies that has finally emerged failed to lift regional traders out of a defensive mode.
The buoyant mood on Wall Street after the deal was announced did not filter down to many bourses in Asia, although Japan kept on its winning ways.
Singapore's benchmark Straits Times Index (STI) closed 0.39 per cent or 12.81 points lower at 3,242.65 on turnover of 2.2 billion shares worth $944 million. Losers outnumbered gainers 236 to 149.
Hong Kong - which resumed trading after Monday's holiday - performed the worst among key Asian markets on weak Chinese factory numbers out on Sunday. The Hang Seng Index dropped 2.4 per cent or 662.14 points to 27,126.38.
The ASX 200 in Sydney ended in the red, as did the Kospi in Seoul, which recorded its biggest percentage loss since Aug 13.
However, the Nikkei 225 continued its run, registering a fresh 27-year high yesterday on upbeat incoming earnings and a weaker yen.
IG sales trader Jayden Loh said: "Asian markets certainly did not share the joy from their US counterparts on the US-Mexico-Canada Agreement. Previously, the Trump administration was fighting trade disputes on several fronts but with the breakthrough, markets may be worried that (Donald) Trump will now focus his attention on China."
FXTM chief market strategist Hussein Sayed agreed, saying a resolution may be on the cards soon "given that United States Secretary of Defence James Mattis cancelled his trip to China later this month".
Nico Steel was the local bourse's most hotly traded stock, gaining 16.7 per cent to 0.7 cent on turnover of 294.9 million shares.
Jardine Cycle & Carriage was the STI's biggest loser in dollar terms for the second straight session, falling 35 cents to $31.50.
In percentage terms, contract manufacturer Venture Corporation was the index's biggest loser, closing 30 cents down at $18.22.
Jardine Strategic Holdings was the index's biggest gainer on the day, adding 1.3 per cent to US$36.96.
Financials weighed heavily on the STI with the three local banks all down.
DBS Group Holdings lost 1.3 per cent to $25.63, OCBC Bank dipped 1.2 per cent to $11.31, while United Overseas Bank ended 1.2 per cent lower at $26.73.
Developer CapitaLand, which has bought a 50 per cent stake in co-working operator The Work Project Kingdom, fell four cents to $3.32.