Wales almost wiped out a 13-point deficit at Twickenham, dominating the final quarter against an England side that required Jonny Wilkinson's trademark drop-goal accuracy to claim a 23-19 success.
England were outscored 3-2 on tries - George North's double and Shane Williams' 54th Test match touchdown ensuring that Wales, unlike before the 2007 World Cup, ran their hosts close.
"We were certainly the fitter team come the end of the match," said Cardiff Blues centre Roberts.
"To come back from where we did and almost clinch it showed we are a strong side.
"But we are disappointed to have conceded two soft tries. (James) Haskell's try off the back of a scrum, maybe we got our defensive set-up wrong there.
"And it was a good line from Manu (Tuilagi) for his try, but our defence was quite weak under our posts, so two soft tries were conceded, really."
Overall, it proved an encouraging afternoon for Wales coach Warren Gatland, whose players showed the benefits of two punishing summer training camps in Poland by finishing strongly.
Roberts' midfield partner Jonathan Davies added: "If we had been playing for another five minutes then we felt we would have won that match.
"We finished the game strongly, but it was frustrating we conceded all the unforced errors and the soft tries we gave away.
"We were disappointed by that, but this was our first game of the season and we can be reasonably pleased with the way we played. We just need to cut out the little mistakes, but we are going in the right direction."
Wales face England again next Saturday, this time in Cardiff, then host Argentina before Gatland unveils his World Cup squad, and competition for places looks like being intense.
Unheralded fringe players such as prop Ryan Bevington, hooker Lloyd Burns, scrum-half Tavis Knoyle and centre Scott Williams all pressed claims by featuring prominently during Wales' dominant closing quarter display.
"I am trying to do all the basics well," said 21-year-old Knoyle, who appears on course to make Gatland's final squad cut.
"If I get an opportunity next week, it's about me pushing hard again. All you can do is try to keep yourself in the mix. The margin for error at this level is so small."
Gatland added: "The players felt pretty good, and as a coach you want selection problems. It is nice to have those discussions in selection.
"I thought the bench made an impression. Ryan Jones did a great job in particular, and we had talked up Scott Williams and he was excellent, too.
"We were able to up the tempo in the second half, and I was really pleased with the energy we showed.
"I thought we finished the game strongly. We are pretty happy with that, we scored three tries to their two."
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