Matt Williams side had their first taste of Six Nations Championship success in eight attempts with an ugly 18-10 victory over Italy on Saturday.
Dan believes restoring confidence was more important than putting on a show and now feels a huge weight has been lifted from their shoulders.
Wales are the next nation in town in a fortnight's time and are looking to continue their Grand Slam glory bid but Dan thinks Scots can throw a spanner in the works.
"We definitely got a bit anxious beforehand just because we haven't won at Murrayfield for a while," said Dan.
"We knew that we needed to win to get the fans back behind us. With this victory that has happened now.
"We definitely improved on the Ireland game and to get a result at this stage is great for the country.
"It is such a relief and now we can go into our next games with the pressure off and with confidence of more success.
"With Wales doing so well it was important to get a win and now the pressure's off us and we will improve again.
"You have to have the belief that you can beat them and this victory will give us a lot of confidence.
"It was nice to get a win. We knew that it didn't need to be pretty. It was just about getting the win because we knew the confidence would come back after that.
"We just needed the win more than anything else. It has been very tough for all of us and that's why it was so important to get the win no matter what.
"You could sense that it has been quite nervous in training but I think you will see that tension lift from us now. Once you taste success you are going to get confidence from it and then you will crave more.
"You need a bit of luck in this championship and in France those things went against us but we are looking forward to building on this and it won't be easy for Wales."