The Foxes played the better football and created numerous chances throughout. However, Stephen Bywater in the Derby goal was not forced to make a save of any note during the goalless draw at the Walkers Stadium.
Pearson accused the Rams of showing a lack of ambition but expected his side to show enough guile to win.
"It's frustrating because they probably got what they came for, so in that sense it's frustrating," said Pearson.
"We didn't ask enough questions of them I suppose, but we were by far the better side over the 90 minutes and were probably the only side trying to win it.
"But this kind of game shows what the Championship is all about. It's a tough league but we expect ourselves to win a game like that.
"They worked hard to break the tempo up but there's no doubt in my mind we were the better side. However, we have to take it on the chin and get ready for the next match against Crystal Palace on Tuesday night."
By contrast, Derby manager Nigel Clough was understandably delighted with a point.
Clough felt his side may even have gone on to win the game had referee Mike Dean agreed with one of two penalty shouts the Rams had in the second half.
"I'm satisfied with a point, certainly after the first half," said Clough.
"They dominated and we didn't cope particularly well with what they were throwing at us and when we did get the ball we seemed to give it away, so it was a relief to get in at 0-0 at half-time.
"Leicester have an extremely good home record and we expected them to come out of the blocks, but we were a bit nervy and it took our defence a while to get to grips with Steve Howard.
"But the second half was much better and just the type of performance we are looking for away from home. We were solid and withstood some pressure but I don't think Stephen (Bywater) has had a shot to save."
Derby felt they should have been awarded a penalty when Jack Hobbs appeared to clip Rob Hulse's heels in the 62nd minute.
They had a second penalty claim turned down after 70 minutes.
Hulse was again involved as Morrison appeared to interfere with him as the two players jostled for position inside the box.
Clough explained: "We thought they were good shouts for penalties, and if we get one who knows, we might have even sneaked a 1-0 win.
"Rob has said he thought his heels were clipped for the first one and the second one we thought was more of a penalty as he seemed to be completely impeded as he went up for the header. Their defender didn't have any intention whatsoever of playing the ball."
Pearson had yet to see the incidents but said: "If they want to clutch at straws on that one then that's up to them.
"I would have to have a look at them before I make a comment on them as decisions, but one thing I do know is that we were the better side."