Referee Martin Fox awarded the Aviva Premiership champions a penalty try in each half of their 20-11 win, the first after two collapsed scrums and the second after 11 scrums had been reset.
When asked if he thought both were harsh, Smith said: "Yes I do.
"You know what you are going to get here. Leicester tried to put us under pressure by continually scrumming us.
"It's difficult. There were a series of scrums and the crowd were as impatient as the coaches. It was difficult to see a great deal of consistency, but I take nothing away from Leicester. They had the intent and wanted to scrum us into the ground and got rewarded.
"We had two opportunities to squeeze a bonus point out of it, one off the tee and a drop-goal, and we came up short, but that's footy. We gave it our best shot.
"I am really proud of the effort from our boys. I thought (captain) George Skivington did a great job leading the troops into battle, and we gave it everything."
Leicester were awarded their penalty tries in the 10th and 64th minutes while England reserve fly-half Toby Flood converted both and kicked two penalties.
Irish replied with two penalties by former Australia full-back James O'Connor and a late try by centre Fergus Mulchrone.
But the Exiles, who lost hooker David Paice with a broken arm and are struggling in 11th place in the table, missed out on a losing bonus point after Darren Allinson hit a post with a conversion and Shane Geraghty missed a drop-goal in stoppage time.
Leicester's win, which ended a dismal run of three league games without a victory, moved them up one place to sixth but came at a cost as centre Matt Smith joined a long injury list after straining a hamstring.
Leicester director of rugby Richard Cockerill said: "The first penalty try seemed to be very quick and it looks like someone had a few words with the referee at half-time and said, 'you can't do that.'
"And the second one was ridiculously long. We can't get any consistency within a game, never mind from game to game.
"We dominated the scrum and if you don't want to stay square and walk round all the time, what is the referee meant to do."
He added: "You have to win your home games and keep chipping away. We needed the four points, but we could not get any shape into our game.
- Sports & Recreation