The Tuscan club had started the day at the foot of the Serie A table, but
The win saw Siena move to within four points of safety and Iachini admits it was a result to savour.
"The guys gave a great performance, you have to play well to beat Lazio," he said on www.acsiena.it.
"We played the game in the right way and are reaping the rewards of the great work we do during the week.
"We had prepared well for the match. We were careful in attack and then good hitting on the break."
Iachini is hoping his players can now go on a winning run as they look to climb out of the bottom three.
"The secret to this success is organisation, intensity and the right mindset to always go looking for a victory by playing proactively," he said.
"We have to continue like this, always believing in the work we do.
"I do not look at our ranking now, it makes no sense to do so. We will just try to win as many games as possible, then we will do the maths at the end."
Lazio remains third in the table but is 11 points behind leader Juventus and without a win in its last five league matches.
He said: "I take the blame for the team and the tactics, but you have to compliment Siena for the way they played. There are no excuses for this defeat.
"I did not need to shout at the players - they are smart and know what they did wrong.
"We also have to apologise to the fans because they did not see the real Lazio."