"Winning back-to-back was the main goal this weekend. We have been consistently inconsistent all season but getting that win, backing up the win against Galwegians last week, was the sole goal of the day," he told IrishRugby.ie afterwards.
Despite having six players on provincial duty the previous night with Ulster, Dungannon director of rugby Justin Fitzpatrick made no excuses following the defeat and was quick to praise Lansdowne.
"It was a very talented Lansdowne side who had just a bit more firepower than us," said the former Ulster and Ireland prop.
"We lacked precision in key moments and it cost us dearly and that is always going to happen against a talented outfit like Lansdowne."
Looking at the calibre of players at Lansdowne's disposal, Fitzpatrick added: "They have a lot of guys with a greater level of experience, guys who have played provincial and top European club football.
"You have Ed O'Donoghue, Eoghan Hickey, John Lyne, Aidan McCullen - there is an awful lot of guys who have played top flight football.
"Today we were not in that position. We have a lot of guys in their first or second season of club rugby."
After leading 13-3 at the break thanks to a converted Matt Healy try and two Eoghan Hickey penalties, Lansdowne stepped it up a gear in the second half with three tries in six minutes which crushed the life out of Dungannon.
"We were probably a little bit over anxious and we tried to kill the game in the first 30 minutes as opposed to looking at the game as 80 minutes," explained Clancy.
"I told them to keep our patience, keep our composure and our accuracy and that the scores would come. Our defence was very strong and as a result of our defence, we turned over ball and created scores from that."
Although it was a fine attacking display by Lansdowne, Clancy was slow to pick out individual performances.
"Ciaran O'Boyle got two and Matt Healy got a couple but it was an all-round team performance. There were no individuals. Everybody set themselves a goal after last weekend to back their performance and that is what we did."
The result consolidates Lansdowne's position in third with three matches left in the regulation phase of the league, but the Dubliners are not looking beyond next Saturday's visit of table toppers Clontarf to the Aviva Stadium
"There is a lot of rugby to be played. We have three games left. We are not looking any further than Clontarf.
"We will get our calculator out on the second of April and tot up the numbers and if we are in the top two, great, and if we are in the top three, great. We are just taking it one week at a time."
While Lansdowne look towards promotion, Fitzpatrick and Dungannon, who are seventh in the standings, will now aim to regroup for the final few games.
"I think there was plenty of positives. I thought our scrum was outstanding, we held the ball for large segments of the game very well," said Fitzpatrick, whose side face Corinthians in their rescheduled Bateman All-Ireland Cup semi-final next month.
"We were just not individually and collectively precise enough to take any more out of the game. We have to look at what we need to tighten up on, but when we reflect on it and look at the video we will realise we were a lot closer than the score implied."
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