Ulster fly-half David Humphreys was in inspired form for Ireland, finishing the match with 26 points, but the Scots were equally to blame for their own downfall as a string of try-scoring opportunities went begging.
Logan made no attempt to excuse his team's performance, but he insisted France should write Scotland off at their peril.
He said: "We've got a lot of work to do after yesterday's match but we must be positive as a team because we face a massive challenge next weekend.
"It's going to be very difficult. We've got to try and stick together and turn things round - there's no getting away from it, we're under pressure now.
"But we've won there before in 1999 which is good. One of Scotland's strengths is that we can go away from home and play well.
"The pressure is on us as a squad but knowing the players as well as I do I think we'll go to France and give a good account of ourselves. We owe it to the coaches, fans and each other."
Sunday's result has given a clear indication that Ireland will be challenging for top honours this year - a point Logan is keen to emphasise.
"They are a good side - if they build up a bit of confidence then they can go a long way. I know exactly what it's like when you're playing in a team full of confidence," he said.
"They've got England and France at home so you've got to fancy their chances and they've got an away win against us which is a big bonus.
"We really thought we could beat them, but they performed on the day."