Brady completed 23 of 36 passes for 239 yards, two touchdowns and two interceptions in the 34-23 loss Sunday at the Mercedes-Benz Superdome. Saints running back Alvin Kamara scored twice in the victory.
"I certainly think [the Buccaneers had] poor execution and that's what it comes down to," Brady told reporters. "It's a game of execution. Obviously, they made more plays than we did and I just made some bad, terrible turnovers and it's hard to win turning the ball over like that.
"I obviously have to do a lot better job."
The Saints opened the game with a punt before Brady marched the Buccaneers down the field with a nine-play, 57-yard drive. The six-time Super Bowl champion ended the drive with a two-yard rushing touchdown for a 7-0 lead. The NFC South squads then exchanged punts before the Saints tied the score at the start of the second quarter.
Saints quarterback Drew Brees threw a 12-yard touchdown pass to Kamara to end that 11-play, 64-yard drive. Brady threw his first interception on the next drive. The Saints capitalized on the great field position and scored three plays later with a Kamara touchdown run from six yards out.
The New Orleans defense stepped up again on the next drive and blocked a Ryan Succop field goal. Saints kicker Wil Lutz then converted on a 29-yard attempt to give New Orleans a 17-7 edge at halftime.
Brady threw another interception to start the second half. Janoris Jenkins picked off that throw and returned it for a 36-yard touchdown to give the Saints a 24-7 lead.
The Buccaneers bounced back with a two-play, 30-yard scoring drive. Brady threw a nine-yard touchdown toss to O.J. Howard to end that drive. Succop then made a 38-yard field goal with 2:27 remaining in the quarter to cut the Saints lead to seven points.
New Orleans responded at the start of the fourth quarter when Brees threw a five-yard touchdown pass to Emmanuel Sanders to push the lead to 14 points with 11:44 remaining. Lutz then made another field goal to extend the lead to 17 points.
Brady threw a two-yard touchdown pass to Mike Evans with 2:46 remaining before the Saints drained the clock on the next drive to pick up the victory.
Brees completed 18 of 30 passes for 160 yards and two scores in the win. Trey Hendrickson, Demario Davis and Carl Granderson each had sacks for New Orleans. Jason Pierre-Paul had a sack for the Buccaneers.
"I thought it was a great team win," Brees said. "We are going to look at the tape and see all kinds of mistakes and obviously we can get so much better in so many areas. But it was a great team win against a really good opponent."
The Saints face the Las Vegas Raiders at 8:10 p.m. EDT on Sept. 21 at Allegiant Stadium in Paradise, Nev. The Buccaneers host the Carolina Panthers at 1 p.m. EDT Sunday at Raymond James Stadium in Tampa, Fla.
"Very disappointing," Buccaneers coach Bruce Arians said. "I would never have thought with the [way] we practiced for the last two weeks -- would have never thought I'd see us have that many penalties, turnovers and just basic mental errors that really cost this one when we got back in the game.
"It's round one -- we've lost round one and we'll get ready for round two."