• Despite the Silicon Valley Bank and Signature Bank failures, most consumers don't need to worry about bank deposits, experts say.
• The standard coverage from the Federal Deposit Insurance Corporation is $250,000 per depositor, per bank, for each account ownership category.
• The bigger risks to investors may be exposure to tech and regional banks, but advisors are warning clients not to make emotional money moves.

After two bank failures and dramatic moves from U.S. regulators to protect depositors, financial advisors have a message for consumers: Don't panic.

The U.S. government on Sunday approved plans to safeguard depositors and financial institutions affected by the collapse of Silicon Valley Bank on Friday. As a result, consumers will have full access to funds from SVB and from Signature Bank in New York, which regulators also shut down Sunday.

The Federal Reserve is also creating a Bank Term Funding Program to secure institutions affected by the instability sparked by the SVB failure.

While futures initially jumped Sunday evening following the announcement from regulators, bank stocks fell as the market opened Monday.

"Every American should feel confident their deposits will be there if and when they need them," President Joe Biden said Monday in an address aimed at easing fears about the U.S. banking system.

Most consumers don't need to worry about deposits

Lee Baker, a certified financial planner and owner of Apex Financial Services in Atlanta, said most consumers don't need to worry about their bank deposits.

The standard coverage from the Federal Deposit Insurance Corporation is $250,000 per depositor, per bank, for each account ownership category, such as single or joint account holders. And you can split cash among ownership categories and banks to avoid exceeding the limits, Baker said.

'A cautionary tale' on diversification

However, the bigger issue for some investors may be exposure to the financial sector. While some may have a smaller slice of exposure through an index fund, it's possible there's greater risk through financial sector-focused funds or individual stocks.

"This is a bit of a cautionary tale as it relates to diversification issues," said Baker, who is part of CNBC's Financial Advisor Council. "I think this can be an illustrative moment for talking to clients."

Still, despite mounting fears, he doesn't believe the bank failures are a repeat of the financial crisis in 2008. "We're not about to head down the road of 40% broad market decline," he said, adding that there's no reason to make "major portfolio moves and panic at the absolute wrong time."

Investors should 'stick to the process'

Ivory Johnson, a CFP and founder of Delancey Wealth Management in Washington, D.C., is telling clients to "stick to the process," explaining that a portfolio should match an investor's goals and risk tolerance.

"If you were conservative before, you should be conservative now," said Johnson, who is also a member of CNBC's Advisor Council. But if your strategy told you to buy tech stocks and regional banks in the current market environment, "it's time to review your process," he said.