Hadden's men were edged out 23-19 by Argentina in the first of their Bank of Scotland Corporate Autumn Tests at Murrayfield after leading for almost three-quarters of the match.
A try and a drop goal from the Glasgow fly-half - in addition to three penalties and a conversion from Chris Paterson - looked to have handed Hadden a welcome success in his first game in full-time charge of the national side.
But number eight Simon Taylor's yellow card for playing the ball on the ground saw the game swing in the Pumas' favour.
The home pack battled manfully in the Lions back-rower's absence but after a series of Scotland infringements in their own 22, referee Kelvin Deaker eventually lost patience and awarded an ultimately decisive penalty try to the Pumas.
Dan said to Sporting Life: "We had the chances to score tries but we just didn't take them. A lot of positives come from the game, that's the important thing, although obviously we wanted the win.
"We played a lot of rugby and gave ourselves chances to score. There were a couple of times we were held up over the line and Jason (White) went close in the corner.
"We did a lot of good things but we just fell short, which is pretty disappointing.
"I think we got to 13-3 and it was feeling pretty good at that point - we just didn't go on and get the tries to put the game to bed.
"We just need to be more patient with the ball. We're creating opportunities, we just need to be more patient and take them.
"We need to look after the ball a bit better but having said that we were very good at the breakdown on Saturday, because we knew we'd need to be good there."
Dan, who qualifies for Scotland through a maternal grandfather from Kilbirnie, enjoyed arguably his finest game in the dark blue.
His fine individual try - as a result of a well-executed chip over the top - capped a commanding first-half performance and he believes things are looking up for Scotland after a couple of years of fairly miserable results.
Next up for Hadden, new captain White and Dan are tough-tackling Samoa - before New Zealand roll into town for what is already looking an ominous fixture.
Dan said: "We didn't get the win against Argentina but next week we'll be up for it. The belief is good, the atmosphere is good and everyone is getting on, which is what you want.
"We can go forward from here, it's just a pity we couldn't hold on for the win because we were ahead for so long.
"It's good fun at the moment and everyone is looking forward to the games. We prepared really well and we showed a lot of good things.
"Argentina pretty much ran the game in the second half, they played the game in the right places. Their forwards took over and they won the game.
"The pack were outstanding when we went down to 14 men and all credit to them but it was just unfortunate that the penalty try was awarded."