Dulos, 52, had been in critical condition from carbon monoxide poisoning at Jacobi Medical Center in New York City.
"To those who contend that Mr. Dulos' death reflects a consciousness of guilt, we say no," Pattis said.
He had declined to comment on his client's condition earlier in the day but on Wednesday said Dulos was in "dire" condition.
Fotis Dulos and Jennifer Dulos had five children together ranging in age from 8 to 13. The kids have been staying with their maternal grandmother in New York City ever since their mother disappeared last May after dropping them off at their school in New Canaan, Conn.
"This is a horrific tragedy all around," Jennifer Dulos' family spokeswoman Carrie Luft said. "Please respect the privacy of the families and loved ones involved."
In a court filing Thursday, Pattis said a note had been found in Fotis Dulos' suburban home in which he "declared his innocence of the infamous and heinous crimes that the state has accused him of and claimed his lawyers have the evidence to prove it."
Pattis and another attorney, Kevin Smith, held a vigil at the hospital earlier Thursday. Dulos' relatives from Greece were believed to be at the hospital.
The day Dulos was found unresponsive in his garage, he had been scheduled to appear before a judge on concerns surrounding the circumstances of his $6 million bond. The insurance company that secured his bond had questioned the assets Dulos used. He used six properties as collateral, but the insurer discovered one of the properties went into foreclosure this past December.
Dulos was arrested for the third time earlier this month in connection to his wife's disappearance. He was charged with felony murder, murder and kidnapping. His girlfriend, Michelle Troconis, and Kent Mawhinney, a local lawyer who represented Dulos in a civil case, were charged with conspiracy to commit murder.
Last week, a Connecticut judge ordered Dulos to strict home confinement after allegations surfaced he took items from a makeshift memorial for Jennifer Dulos. The judge told Fotis Dulos that if he violated the conditions of his release again, he would double the bond to $12 million.
Piercing together what might have happened to Jennifer Dulos has taken investigators on an exhaustive nine-month, multistate probe involving K-9s, state police, drones and even a New York State Police helicopter. They've rooted through tons of trash at a Hartford dump and looked in high grassy areas as well as in shallow ponds for the missing mother.
In a 35-page arrest warrant, investigators alleged Jennifer Dulos was killed at her home on May 24 between 8:05 a.m. and 10:25 a.m. That same day, surveillance footage showed someone in a dark hoodie riding a bike that looked like Fotis Dulos' from childhood toward Jennifer Dulos' New Canaan home. Surveillance video also showed someone driving Dulos' car leaving her house at 10:25 a.m.
Investigators also said Fotis Dulos' DNA was discovered on the doorknob of the mudroom in Jennifer Dulos' home as well as in a garbage bag police recovered from a trash can in Hartford, where investigators claimed Dulos dumped evidence of his crime.
Other items listed in the affidavit allegedly linking Dulos to the crime included bloodied zip ties.
James Bergenn, a criminal litigator at the Shipman & Goodwin law firm in Hartford, told Fox News that prosecutors "will be thinking long and hard about what to do with the other folks, who were, by all public information, not actually involved in the killing."
He added, "The person who is cunning enough to take his own life without anyone predicting it is more likely someone who acted on his own, so prosecutors have some thinking to do about others who sat down with the prosecutors and gave their information."
Bergenn said he's known Pattis professionally for 30 years and wouldn't rule out a wrongful death civil suit brought by Jennifer Dulos' family "if the family needs some kind of a judgment, like the Goldmans and OJ."
Fox News' Laura Ingle contributed to this report.