In a low-scoring Pool Five opener at the RDS, three penalties from Jonathan Sexton were enough to earn hosts Leinster a 9-6 victory despite a below-par display.
Exeter had a chance to draw the tryless game right at the end, but Argentinian replacement Ignacio Mieres missed a long-range penalty.
Speaking afterwards, Schmidt lauded Exeter's performance while admitting his side have a few things they need to work on.
He said: "It was no surprise to us how tough they (Exeter) were to break down. As I've said all week, I think they are a formidable side.
"They are greater than the sum of their parts. I just think they are a very unified group. They're well coached, they're well organised and they're hard to break down.
"Having said that, it's not often we get in the 22 four times in the first half, and get nothing from it. That's down to us, we have to be more accurate than that.
"We were a little bit inaccurate and we have got to be patient enough to build scores against a really good team."
As they aim to secure a fourth European Cup in five years, Leinster will certainly be looking to step up their performance level for the remainder of the group stage.
However, though this game was a lot closer than many would have anticipated, Schmidt still felt that there were positives to take from it.
"One really good positive is that it's our first game this season where the opposition hasn't scored a try. That is a real positive to take out of it," he said.
"Obviously, if we had conceded one, we wouldn't have won. So, you've got to start with a couple of positives, and a couple of 'work ons'.
"We'll be taking a sample of those during the week and try to work our way through them," added the New Zealander, whose side visit the Scarlets next
In contrast, Exeter boss Rob Baxter was extremely pleased with his side's efforts in what was their first-ever Heineken Cup appearance, and felt they were unlucky not to get at least a draw.
"I think we're disappointed not to win, but I'm pleased with the level of performance. We were good at times today," he said.
"We still made some mistakes that cost us a chance of what would be a very, very important win.
"There was a little bit of everything in the game. We're a little bit unfortunate not to come away with a win or a draw. At the same time, we are pleased with large parts of our game."
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