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On Thursday, Financial Timesreported the kingdom was claiming success over its rivals like the shale producers.

"There is no doubt about it, the price fall of the last several months has deterred investors away from expensive oil, including U.S. shale, deep offshore and heavy oils," a Saudi official told the newspaper.

Read MoreUS shale has 'blinked' in OPEC battle: IEA

For Kilduff, the comments confirm the suspicions many had about the Saudi's decision to not cut production levels in response to falling oil prices.

"It shows that they were doing exactly what a lot of us had speculated about—trying to squeeze out the high-cost producers," he noted.

Meanwhile, Saudi Arabia is nearing its productive capacity, pumping over 10 million barrels of oil a day, Kilduff said, noting that the kingdom claims to have 12.5 million barrels per day of capacity.

He thinks Saudi Arabia's inability to keep prices really low calls into question its ability to break the back of the market.

That said, he still believes oil prices are headed lower again later this year.

Leo Mariani, energy analyst with RBC Capital Markets, thinks the Saudis got what they wanted short term.

"There's no doubt that we've seen debt levels balloon up over the last several months as oil prices had made their way down. So certainly the balance sheets are modestly impaired compared to what they used to be at $90 to $100 oil," he told "Power Lunch."

Read MoreThe oil rally's winners and losers

However, he doesn't think there has been any permanent damage.

"I believe that you'll see these companies continue to grind out efficiency gains and be able to execute on their business plans to the extent that we see oil prices modestly higher over the next year," said Mariani.

However, if Saudi Arabia decides to increase production, he believes there will be continued modest pressure on oil prices.

He's bullish on select shale producers, such as Apache, EOG Resources, Newfield Exploration and Pioneer Natural Resources.

—CNBC's Stefanie Kratter contributed to this report.

Disclosures: Apache Corporation, EOG Resources and Newfield Exploration are investment banking clients of RBC Capital Markets. RBC is currently providing Apache Corporation, EOG Resources and Newfield Exploration with non-securities services. RBC Capital Markets is currently providing Pioneer Natural Resources with non-securities services.

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Too early for Saudis to declare victory over shale: Analyst