Tom Brady wants the Tampa Bay Buccaneers to show a greater killer instinct after missing chances in their road win at the Washington Football Team.

The Bucs won their first postseason match since the 2002 campaign on Saturday, beating Washington 31-23 in their first playoff game in 14 years.

Brady threw for 381 yards and recorded his 75th career postseason touchdown after setting up Antonio Brown and Chris Godwin.

The 43-year-old, now the oldest player in history to throw a touchdown pass in an NFL playoff match, dropped deeper to pick his targets and frustrate a Washington pass rush that recorded 47 sacks in the regular season.

Brady, who led the regular-season standings for downfield passes of 20 yards or more, threw for two touchdowns over the same distance in a postseason game for the first time in his remarkable career.

Still, he was frustrated at certain missed opportunities, notably when he was sacked by Daron Payne and when Godwin made three drops, which allowed Washington nine unanswered points in a third quarter that threatened to derail the Bucs' endeavours.

"We hit some big plays, made some chunks," Brady said. "I think just not scoring enough in the red [zone] was probably the thing that bothers us, [we] missed a two-point play, had other opportunities to score but just didn't quite take advantage of it.

"We moved the ball okay. I think we had decent yardage. But at the end of the day, it comes down to points, and we've got to do a better job scoring more points - and we'll work on that next week."

Brady was full of praise for wide receiver Mike Evans, who recorded a team-high six catches on 10 targets for 119 receiving yards, all after recovering from a hyperextended knee in Week 17.

"Mike played his butt off," Brady said. "He got hurt last week. We weren't sure if he was going to go or not. [He] just did an incredible job fighting through it and made a bunch of big plays when we needed it."

The match mostly belonged to Brady, though, the six-time Super Bowl winner making history as he became the oldest player to throw a touchdown pass in the playoffs, overtaking George Blanda in the 1970 AFC Championship game.

"Come on, that's Tom Brady," said team-mate Leonard Fournette said. "I haven't got to think too much about that. That's the boy. We've got faith in him. We're going to protect our butts off for him to make sure he gets that throw. That's our job."