'Tarf were playing into a strong gust in the first half but that could not be blamed for the numerous turnovers which allowed Mary's to control the play.
The towering dominance of second row Copeland was decisive for Mary's as he proved to be a constant menace for 'Tarf particularly in the lineout and at the breakdown.
Speaking after the match, Copeland said that the result did not come as a surprise.
"Our preparation has been good all week and from the moment we arrived (today), we were ready for the challenge," he admitted.
"We couldn't have picked a better team to start the campaign against but it's good to come out on the winning side."
Copeland was the first to react after Gavin Dunne's 10th minute penalty struck the post and he collected the ball to score Mary's first try under the posts.
He then went on to score his second try and Mary's fourth just shy of the half hour mark, when he picked the ball from a ruck and with sheer force managed to break through a tackle and burst for the line.
Clontarf started the second half in better form through a rejuvenated pack, however, all they could muster was a single try in the 55th minute when Michael Keating broke through the cover and offloaded for Sean Carey to finish off the score.
The north Dubliners, who have Bernard Jackman as their new director of rugby, did threaten their opponents' try-line up until the final whistle but the Mary's defence showed great character to hold firm.
Potts told IrishRugby.ie: "This performance was coming all the time and when we played Lansdowne two weeks ago we put in a top performance then, so we knew we were going to bring that into this opening AIB League game.
"We were saying all week if our attitude is right and if we believed we could come out here and win, then we would do the job."
In the starting line-up for Mary's were new signings, Gavin Dunne at full-back and Joe Burns at scrum half, who proved their worth as they both played key roles in an impressive, restructured back-line.
"Our new signings are still working their way into the team, they're still getting used to how we play but anyone we've brought in has really stepped up to the mark and they're showing good value," added Potts, the former Leinster flanker.
Next up for Mary's are two tough away matches against Shannon and Garryowen. Potts will be looking to build on this opening win but preparation will be key if they want succeed against the Limerick heavyweights.
"Every game is going to be tough in the top eight, we will take each game at a time.
"Next up is Shannon, they lost to Garryowen on Friday but you know, we're not going to get carried away with ourselves, We're going to train hard and bring everything we can into next Saturday's match."