The Tigers built up an early 14-0 lead and seemed in control but they allowed a battling Irish side a foothold in the game through three penalties from Ian Humphreys.
A penalty from Toby Flood and two late converted tries gave Leicester what was at least on paper a convincing win.
Smith said: "I'm really disappointed as we came up short again. I'm proud of the boys' effort and we deserved a bonus point, so to come away with nothing was harsh."
It was 17-9 to the Tigers when the visitors sealed victory with a crucial penalty try in the 73rd minute.
Niall Morris broke away from on halfway and kicked ahead. He would have secured the try himself but was taken out by Irish replacement Jamie Gibson, who was yellow-carded before Flood added the conversion.
Smith was far from happy to concede the score.
He said: "The third try was the game-breaker for us. There were clear hands in the ruck to wrestle the ball free to give Leicester their opportunity and when the penalty try was awarded it was game set and match."
Irish certainly did not appear to have the rub of the green with the refereeing decisions. Tom Youngs should have received at least a yellow card for recklessly charging into a ruck but he only received a warning from referee Luke Pearce.
"Tom Youngs shouldn't have played the full 80 minutes," said Smith. "There were no arms involved and it was a shoulder charge which nearly took Declan Danaher's head off. It was perhaps a red-card offence and the citing commissioner will have to have a look at it."
Smith's Leicester counterpart, Richard Cockerill, agreed the scoreline was not an accurate reflection of the game.
"We were fortunate," Cockerill said. "The boys scrambled well but they [London Irish] played pretty well today and they deserved a bit more.
"We were really good in the first half and had several opportunities but we didn't take them. We then sat back and waited for things to happen which was disappointing, but it's five points on the road."
Flood returned after over a month off with a toe injury and was rewarded with 11 points, and in addition he created the first try for Morris with an alert cross kick.
"Toby was very assured today; it was a quality penalty kick under pressure late on and his kick to Niall was great awareness." said Cockerill.
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