With Edinburgh also flying high in the league standings, many saw the Scots as favourites heading into the clash, but tries from George Kruis and Jack Nowell were enough to see England to a 15-9 triumph.
And Hardie, who was making his Six Nations debut, is adamant his side can challenge alongside the home nations if they nail down their execution.
"We showed some really good facets in attack and we held the ball," he said. "A lot of our kicking was good at times and our backs really inserted pace into the game. But the wee opportunities were just that far off from being completed.
"It's a great group of boys - we could do some good things. At international level, it's just those little things and being really ruthless. It's decision making and all that sort of stuff.
"It comes down to execution and, individually, you have to look at what you have to do to help the team. Cut those errors out and then you'll start to click.
"We need to learn from the mistakes we made and have a look at the tape of the game, see what we did wrong and start to look forward to facing Wales in Cardiff."
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