Financial markets' quiet response to the latest Greek crisis shows how much things have changed since worries about Greek debt helped disrupt global markets in 2011 and 2012.

Money managers have become more confident in the ability of the European Central Bank and U.S. Federal Reserve to deal with this kind of crisis and in the ability of the global economy to withstand it. That view was reflected in markets on Monday, following Greece's vote Sunday rejecting creditors' demands for pension cuts and tax increases.

Frankfurt's main stock index fell 1.5% and France's, 2%, but it could have been a lot worse. Britain's FTSE 100 was down just 0.76% and the Dow Jones Industrial Average fell only 46.53 points, or 0.26%, to 17683.58. That left the Dow just 3.4% short of its May record. The S&P 500 fell 0.39% and was 2.9% off its record.

The euro fell 0.5% against the dollar, less than many people expected.

"The ECB is playing a much stronger role today than they were several years ago," when money managers weren't sure whether Europe's central bank had the clout to support the Continent's banks and financial system, said Mark Freeman, chief investment officer at Westwood Holdings Group Inc., which oversees $21.9 billion in Dallas.

In 2011, the ECB's ability to buy up troubled countries' bonds to stabilize the bond market was the subject of intense debate, with many German leaders opposed. Last year, the ECB faced German opposition to plans for more than $1 trillion in bond purchases aimed at stimulating Europe's economy. The ECB won the right to carry out both programs and many money managers today judge both as successes. The ECB, once viewed with suspicion, today is viewed by many investors with a respect approaching that accorded to the Federal Reserve.

"There is a lot more confidence in the ECB" today, said David Joy, chief market strategist at Ameriprise Financial Inc., which oversees $815 billion. Greece represents just 1.8% of the economic output of the countries that use the euro, and private-sector exposure to Greek debt has fallen dramatically, he noted. Even if Greece leaves the eurozone, investors could be ready for it, he said.

Not everyone agrees with that. Because of the ECB's success in stabilizing European finances and stimulating the economy, many investors still hope it will find a compromise, avoiding a messy default and possible Greek exit.

There is no guarantee that this will happen, said Mr. Freeman of Westwood, and if the ECB fails to find a compromise, U.S. and European stocks could fall harder.

In 2011, amid worry that Europe's central bank wasn't prepared to deal with the debt crisis among its weaker countries, and with Standard & Poor's cutting its rating for U.S. sovereign debt, both the Dow and the S&P 500 came close to a bear market, defined as a decline of 20% or more.

This time, nothing like that is happening, in Europe or the U.S. One big reason is that countries like Portugal, Spain, Ireland and even Italy have made their economies more competitive, something that has Greece has had trouble doing.

Financial markets' confidence in these other less-solid European economies can be seen in their government bonds, which have suffered relatively little as worries about Greece have spread, said Leo Grohowski, chief investment officer at BNY Mellon Wealth Management, which oversees $194 billion. Spreads, or the difference between these countries' bond yields and those of stronger countries such as Germany, "have not widened out as much as they would have if there were a feeling that there are more shoes to drop," Mr. Grohowski said.

Investors also said they have confidence that the Fed will raise its own target interest rates only if it is confident that the U.S. and global economies are solid enough to shrug it off.

Some think the Fed will postpone its first rate increase, which had been widely expected in September. Others think that will be unnecessary.

"Fundamentals in the U.S. remain equity-friendly," Mr. Grohowski said, noting that inflation is low and second-half earnings expectations remain positive.

One reason U.S. markets have reacted mildly to the Greek referendum is that money managers see little direct impact on U.S. corporate earnings.

"Greece is kind of front and center but to me China is a bigger issue and the earnings outlook for the second half is bigger than either one," said Mr. Freeman of Westwood. He is unsure about China's problems, he said, but he remains hopeful that earnings will rebound in the second half, permitting stocks to continue rising.

Charles Schwab & Co.'s chief global investment strategist, Jeffrey Kleintop, went a step farther in a report to clients. "There have been a number of developments unrelated to the situation in Greece that we believe may be at least as important to the direction of markets in the second half of 2015," he wrote.

"The five developments you may have missed in the past week include: rising manufacturing activity in Europe, recovering home prices in China, an increase in the oil rig count, a rebound from deflation in Britain, and improving business sentiment in Japan."