While England emphatically took their chances to cross, Chris Ashton notching twice, the home side managed just one score through returning winger Morgan Stoddart.
And Roberts - who was uncharacteristically quiet on the night - believed that the welsh decision making had cost them in a tight affair in Cardiff.
"In the key moments we weren't accurate, we kicked the ball out on the full a few times and that cost us," said Roberts.
"It was a nothing kick that led to the first try really and with ten minutes to go we put the ball straight out on the full and we were immediately under pressure again.
"So there are a few game management issues that we need to work on for next week but it was a close game and someone has got to lose and it was us and we are gutted.
"Losing that closely is always more disappointing. I have been in some of those games and won in the past and that shows in international rugby the margins between winning and losing are incredibly small and the little things matter hugely and unfortunately we just didn't box clever."
Warren Gatland's side will now need to come out on top in a potentially tricky trip to Scotland next weekend to get their RBS 6 Nations campaign off and running.
But Roberts believes, with the last trip to Murrayfield ending in a 26-13 win for the Welsh, the side have the knowhow to produce the goods in Scotland.
"I think we can take a lot of heart from the way we defended and especially our goal line defence because the line breaks we conceded were minimal," added Roberts.