Tries from backs Danny Care and Luther Burrell and the boot of Owen Farrell saw England claim victory, pulling clear in an entertaining game.
The boot of Leigh Halfpenny, who kicked six penalties, kept Wales in the game but it was Stuart Lancaster’s men who came out on top to claim a first Triple Crown since 2003.
“We had too many errors and too many turnovers, England capitalised and scored the points,” said Faletau.
“We’re disappointed. The errors are what cost us the game but England played well and took their chances.”
Care’s early try from a quick tap penalty gave England momentum with Burrell’s score extending their lead. Five penalties from Halfpenny meant Wales only trailed by five going into the break but in the second half, Farrell’s boot guided England home.
“England got momentum building pretty quickly and we just couldn’t quite get there,” Faletau added.
“We were aware of Danny and his quick tap penalties but we couldn’t react quickly enough. England were always one score ahead but we were in the game until right at the end. We just couldn’t quite breach that gap.
“We wanted to come away with the Championship and it’s disappointing not to be able to do that.”
After defeat at Twickenham, Wales face a quick turnaround ahead of Saturday’s game with Scotland.
“We want to win against Scotland and end the tournament on a good note,” Faletau argued. “We need to work on what went wrong against England looking ahead to this week.
“We’ll go back to basics and hopefully we’ll be better going into the next game. Kicking was something we worked on during the week but we couldn’t quite execute what we wanted to and it cost us the game in the end.”