They may have outscored the hosts by three tries to nil, but Ireland's overall display was noticably below par and a world away from the form they hit in the autumn.
Taking the positives from the opening weekend's win, Horan said: "A win builds confidence, but we have to move on. There was a lot of pressure on us leading into the game in Cardiff and nerves probably showed in the first half from everybody.
"It's always hard being the first game and it's even harder when you're sitting in a hotel watching the other four teams playing first. You just want to get the game under way.
"The Six Nations has started for us and we got the result we wanted if not the performance. There were some good aspects that came from it."
Asked about the scrum - an area in which Ireland and the provinces have come in for some considerable criticism in the media - the Shannon clubman countered: "To be honest there has never been an issue with the scrum. We have always been confident. The issues have come from guys like yourselves (the media).
"There have maybe been a few glitches with the provinces along the way but you will always have a bad day at the office. We are not going to be shouting from the rooftops that everything is brilliant.
"We are setting our targets one game at a time. We are over the first one, it went well and the scrums were 100 per cent. You couldn't ask for anymore."
With the focus switching to Croke Park this week and Ireland's historic first outing at the Jones's Road venue, Horan knows there is considerable scope for improvement and a big chance to end a four-match losing streak against Les Bleus.
"We prided ourselves with our defence against Wales, but we are also well aware that France will punish us if we make any small mistakes," Horan added.
"No disrespect to Wales, but we can't afford to give up ball as easily as we did last Sunday, because the French are such good counter-attackers and finishers."
Ahead of one of the most anticipated fixtures in Irish rugby history, Horan relayed the feelings of the squad, saying: "It's every Irish kid's dream to play at Croke Park no matter what sporting background you're from. "We all had a great sense of pride just walking into the place for training last week and I think that pride is going to be even greater against France.
"It's a great occasion and it's fantastic that the GAA have done this and allowed us to play there. It would have been an awful shame if we'd had to have played our international games abroad."