“Leading up to the draft, I provided every interested NFL team with all the information asked of me about football and my personal life,’’ Hernandez said in a statement issued yesterday by the Patriots. “I was as candid as I could possibly be about everything, including my one single violation of the team’s substance testing pol icy over the course of three years at the University of Florida.

“That is why I was very surprised and disappointed by the recent inaccurate report of additional violations. I regret what happened, I learned from it and will make better decisions going forward. I couldn’t be more excited about beginning my NFL career and representing the New England Patriots well.’’

The team declined further comment.

Sources from five NFL teams have told the Globe that Hernandez failed multiple drug tests at Florida for marijuana. Three of those sources were cited in Tuesday’s story; yesterday, sources from two other teams confirmed the report.

One official contacted yesterday couldn’t confirm the exact number of positive tests, but said, “It was absolutely, positively more than two.’’

Hernandez missed the Gators’ 2008 opener against Hawaii and a November 2009 game against Florida International. No explanation was given for his absence in the Hawaii game. After the game against FIU, Florida coach Urban Meyer said Hernandez “wasn’t ready to play’’ and didn’t give a further explanation.

Privacy laws prohibit the school from commenting on drug tests.

Florida’s drug-testing policy mandates counseling and further testing for one positive test, a one-game suspension for a second positive test, a two-game suspension for a third positive, a six-game suspension for a fourth positive, and an indefinite suspension for a fifth positive.

But the Palm Beach Post reported yesterday on loopholes that exist within the policy, allowing for significant discretion on the part of university president Bernie Machen and athletic director Jeremy Foley.

The Post reported that Foley and the school’s substance abuse committee — staff members appointed by Machen — “may recommend a reduction of sanctions’’ at their discretion.

Foley has the power to review new information and reduce penalties under the policy, with conditions for such a reduction as follows: student’s response to the previous positive test; response and consistency in attending counseling; devotion to academics; and time given to Goodwill Gators, the school’s community outreach program.

The Post also reported on this loophole: “Athletes are subject to penalties if their urine contains 15 or more nanograms of THC, the active drug in marijuana, per milliliter. A positive result of 5-14 nanograms per milliliter results in unspecified penalties, but no suspensions.’’

Hernandez was considered by many to have the talent to be selected late in the first round or in the second, absent these issues.

A source close to Hernandez, independent of the five aforementioned sources, told the Globe Monday night that Hernandez’s marijuana use was the reason he dropped to the fourth round. The source added that, to his knowledge, the player failed just one drug test.

But an AFC college scout said Monday night, “It’s not like he failed one test. He had repeated issues with it, to the point where you worry about whether he’ll be able to lay off the stuff at our level. To be honest, he’s super-talented and, even with the issues, I’m surprised he fell as far he did.

“Depending on who you talk to, some people thought he was a late first- or early second-round prospect. Eventually, the risk was overcome by the value.’’

Albert R. Breer can be reached at abreer@globe.com. Follow him on Twitter @albertbreer.