Irish's relegation from English rugby's top flight for the first time since 1994 was confirmed on Sunday after a 32-25 home defeat by Harlequins.
"We've got to learn from those mistakes," Narraway told BBC Radio Berkshire. "Moving forward, we've got to make sure we eradicate them."
The Exiles will play Championship rugby next season as they bid to bounce back.
Narraway also lamented how a 17th defeat of the season came despite an encouraging performance against Quins.
"We've probably played good enough to win the game," he added. "I don't think anyone can argue with that.
"We were probably the better side at Newcastle and, apart from five minutes, the better side against Quins.
"It's difficult to take. I've never been relegated before in my career.
"I'm fully committed to the club. It's got great staff, great players and great people behind it. We've just let ourselves down at certain moments of this season.
"We'll stick together and hopefully in 12 months' times, we'll be building towards another Premiership season."
London Irish captain Luke Narraway says the club's players all believed they could avoid Premiership relegation.