"If we have the ball then we know that we can attack, but I thought today was a superb defensive performance," said the Heineken man of the match.
"I think we matched Leicester in the pack and it's important that we take it step by step because we have a very difficult pool with three good contenders.
"It is clear now that we have good strength in depth and we're all pleased with the win. I love playing with Leinster - we have really good players and they're really good people also."
Contepomi's haul dwarfed that of his opposite number Andy Goode who could only add a single penalty in the second half.
Two Goode penalties had Leicester leading by 6-3 before Contepomi levelled before the break and then the home side took off in the third quarter, racing 19-6 clear.
After an inconsistent start to their Magners League campaign, Leinster may just have turned a corner and their Australian coach Michael Cheika, in his third season at the helm, expressed his satisfaction with the performance afterwards.
"The players knew what they wanted to do but it's one thing saying what you're going to do and another thing making it happen," said Cheika.
"The control pleased me. We showed composure.
"In the past maybe we've been a bit guilty of going for too much. This time we tried to balance the opportunities to go and the opportunities to build field position. That's the standard we want to set for ourselves.
"There were a lot of good points from today (Saturday) but we understand that we're up against another international front row next week in Toulouse. We've got to make sure that our pack keeps their consistency because only then will we be a team that gets through the pool first of all and on further.
"The way this pool is we could play like that today in our away matches and not get anything out of it."
Leicester's new coach Marcelo Loffreda, who only arrived at Welford Road earlier in the week after guiding Argentina to third place at the World Cup, maintained a watching brief today with Richard Cockerill in charge of team matters.
Loffreda agreed: "Yes, it was difficult for us. We had (to take) a lot of pressure.
"Leinster played really good. Felipe played really smart. They not only put pressure on us but were very efficient when we had the ball. We got a bit repetitive in our game. We need to change some things for this week.
"One of the errors was that we were going too quickly to ground. In the second half that was important when we trying to get back in the game.
"We didn't play well in the lineout either. We will have to work hard this week. The players will need to be patient with me and I will be patient with them. We will come together on Monday."
Pat Howard's successor felt that Leinster's strong defence, which saw them keep the Tigers at bay during concerted spells of pressure in both halves, was key to their victory.
The Argentinian said: "We had a lot of pressure but Leinster played very well.
"They were very efficient when we had the ball. We were not so bright in the first half and we didn't use the wind as well as we should have. Leinster did that quite well in the second half and I think that was a big difference."