The Scots conceded six tries in Dublin as the Irish side maintained their 100% league record.
Cockerill admitted to the club's official website that he had no complaints about the end result. “The better team won on the night,” he said. “I was probably more disappointed that we didn’t score four or five tries ourselves – we had more than enough opportunities.
“If you give them cheap field positioning and let them in to your half - and we let them into our half on plenty of occasions – then they are an experienced and talented enough team to punish you.
“Although the final scoreline was perhaps a bit flattering for them, I was just disappointed at a few parts of our game. We should have at least taken a try bonus-point away from the game.”
The visitors took the lead just after the half-hour mark but despite Leinster losing two players to the sin bin, they could not hold on to a half-time lead.
In the second half Leinster dominated as Edinburgh struggled to cope with the physicality of their hosts.
Cockerill said: "When they had both their prop (Bent) and centre (Tomane) in the bin, that period was crucial. We weren’t particular smart in the way we played.
“We continued to put pressure on their scrum, when perhaps we should have got the ball into the hands of the backs and had a crack at them.
“But we’ve got to learn on the job and makes these changes as the season goes on. We’ve got some inexperienced guys in the team and a relatively new group.
“We should have taken some better options tonight, but we created enough opportunities and put a really good Leinster team under serious pressure.
“So, there are parts of our game where we can take some positives, but the scoreboard doesn’t lie. 40-14 and they were the better team tonight. Leinster deserved to win, but I’m just disappointed that we leave with nothing because I feel we created enough opportunities to leave with two points.”