A rally fizzled out after less than an hour in Europe’s markets Monday as relief over Greece’s election result was overshadowed by concerns over Spain’s high level of debt and overall lack of leadership on the continent.

“Markets simply want someone to take responsibility and at the moment what we have instead is just a high-stakes game of pass the parcel,” Jeremy Batstone-Carr, director of private client research at Charles Stanley, told CNBC.com

Borrowing costs rose for both Spain and Italy, underscoring how tight finances are for eurozone countries as they face an economic downturn. The yield on Spain’s 10-year government bonds jumped to a new euro-era high of 7.14 percent and Italian bond yields rose to 6.08 percent, according to CNBC.

“There is nothing from European leaders,’’ said David Buik, partner and markets analyst at BGC Capital Partners. G-20 leaders meeting in Mexico this week "will utter a lot of platitudes but provide no hard policy or way forward,” he said. "The current outlook is terrifying.’’

However, ETX Capital's senior trader Markus Huber, warned in a note to clients against reacting too quickly to higher Spanish and Italian bond yields following sharp rises in early trade.

"As soon as there is less uncertainty regarding one main issue affecting markets, attention quickly turns to the next one, similar to the situation after the Spanish banking rescue last week where focus shifted onto Italy and Italian banks,” Huber said.

"Although the problems Italy is facing in the form of high debt levels and slow growth are well known, for the focus to fully shift on Italy, something else will be needed, for example, that implementing of urgent financial reforms is being delayed," said Huber, according to CNBC.

Europe should "boot Greece out of the eurozone,’’ said Buik. "The Greeks can’t meet the terms of the bailout agreement. The quicker we recognize it the better, and the rest of the world would look at the EU and say they were finally dealing with the problem.’’

Both Batstone-Carr and Buik indicated they saw little chance of Greece meeting its bailout commitments despite election results which damped expectations that Greece would leave the euro.

Moreover, the election of Francois Hollande as president of France last month and German chancellor Angela Merkel’s own re-election prospects next year had caused political paralysis to settle across the continent, said Buik.

Meanwhile, the Institute of International Finance wrote in a report to its members that the recent 100 billion euro ($125 billion) bailout of Spain's banks would leave Europe's financial rescue fund without enough money to bail out another big economy, CNNMoney reported.

Following the 100 billion euro commitment, "the Eurogroup's rescue funds, as currently authorized and structured, will have sufficient funds to help a small economy like Cyprus, but hardly enough to deal with any large country," said the report.

The IIF was the lead negotiator on behalf of the private sector in the restructuring of Greek government debt earlier this year.

The rise in Spanish yields above the 7 percent threshold raises concerns about Spain’s ability to fund itself, increasing the risk of a government bailout, CNNMoney reported.

"Investors evidently think that, welcome as the Spanish bank assistance package is, important measures still need to be taken to address the growth deficit in current policy approaches in many euro area countries," the IIF report said. "Lack of growth would make debt unsustainable in many cases."

While estimates of the size of the so-called firewall have ranged from 500 billion to 800 billion euros, "in reality" the European Stability Mechanism will have only 16 billion euros in "paid-in capital" in the first three months after it launches in July, the IIF report said.

This would give the fund a lending capacity of up to 107 billion euros, according to the IIF. Adding the remaining funds from another rescue fund, the European Financial Stability Facility, means the EU has a total of 351 billion euros to lend.