Sydney closed 0.84 per cent down, Seoul dropped 1.27 per cent. Shanghai was up 0.71 per cent and Hong Kong lost 0.37 per cent.
Tokyo was closed for the first day of a three-day holiday.
"Osama bin Laden's death was overshadowed by renewed concern about European sovereign debt, particularly in relation to Greece," said RBS Morgans investment adviser Chris MacDonald in Sydney.
Hong Kong had spent much of the day in positive territory before dropping in the last hour of trading to close at 23,633.25, down 87.56 points.
Seoul, where the KOSPI lost 28.23 points to stand at 2,200.73, was hit by profit-taking.
Chinese shares reversed early losses as concerns over further tightening measures eased with data showing manufacturing growth slowed in April, dealers said.
The Shanghai Composite Index, which covers both A and B shares, ended 20.68 points higher at 2,932.19 on turnover of 102.7 billion yuan ($15.8 billion).
Stocks in Sydney fell, with a strong Australian dollar weighing on sentiment over upcoming corporate earnings results.
The benchmark S&P/ASX 200 was down 40.7 points at 4,784.6.
"The market is uncertain as to how big and widespread these downgrades may be, hence the cautiousness we are seeing in trade at the moment," said Ben Potter from IG Markets.
"Markets hate uncertainty, so we're likely to see this continue until some clarity prevails."
The Australian unit weakened to $1.0904 after having surged through the $1.10 mark on Monday.
The country's central bank on Tuesday left interest rates on hold at 4.75 per cent, as widely expected, but warned of possible rising inflation over the longer term as the economy improves.
One euro bought US$1.4817 in afternoon Asian trade compared to $1.4824 in New York on Monday.
Both currencies weakened against the yen, with the euro trading at 119.86 yen from 120.30 a day ago and the greenback changing hands at 81.00 yen from 81.10.
"News of the demise of terrorist mastermind Osama bin Laden gave lift to the US dollar," US-based forex research firm DailyFX said in a report.
"(But) the dollar's move lacked conviction and the greenback is likely to see further weakness on diverging interest rate expectations and concerns over the ballooning US deficit," the firm cautioned.
US stock markets closed flat Monday after initial euphoria over bin Laden's killing faded and investors looked instead to an underlying weakness.
The Dow Jones Industrial Average slipped 3.18 points (0.02 per cent) to finish at 12,807.36.
The Nasdaq Composite dropped 9.46 points (0.33 per cent) to 2,864.08, while the broad-based S&P 500 index retreated 2.39 points (0.18 per cent) to 1,361.22.
All three indices had opened the session with gains after the late-night announcement Sunday that US forces had killed the Al-Qaeda mastermind at his secret compound in Pakistan.
"A lacklustre report on manufacturing took some of the wind out of the bullish sails, with stocks dipping their toes in the red around midday" and closing with modest losses, said Andrea Kramer at Schaeffer's Investment Research.
Oil eased in Asia as traders digested news of bin Laden's death, but analysts warned prices will be tied to unrest in the Arab world and the dollar's value in the long run.
New York's main contract, light sweet crude for June delivery, was down 50 cents to $113.02 and Brent North Sea crude for June eased 42 cents to $124.70.
"(Oil) is holding relatively flat, but oil markets remain vulnerable to geo-political risks with or without bin Laden... and the low value of the US dollar," Victor Shum, a Singapore-based analyst with energy consultancy Purvin and Gertz told AFP.
Gold closed in Hong Kong at $1,542.50-$1,543.50, sharply down from the peak of $1,577.57 it hit in New York trade on Monday.
In other markets:
-- Manila closed 0.17 per cent lower Tuesday as investors took profits in the absence of fresh leads a day after the market hit a fresh six-month high, dealers said.
The composite index shed 7.39 points to 4,319.37.
-- Taiwan's weighted index fell 61.79 points or 0.69 per cent to 8,946.08.
TSMC rose 1.91 per cent to Tw$74.6 while Hon Hai fell 2.31 per cent to Tw$106.0.
-- In Wellington, the NZX-50 index fell 0.08 per cent, or 2.75 points, to 3,495.11.