Irish started brightly at Welford Road, scoring eight points in as many minutes thanks largely to a try from Anthony Watson.
Leicester quickly responded to build a five-point lead at the break, scoring two penalties and a debut try from Rob Andrew.
Tigers fly-half George Ford took control of the game early in the second half, proving lethal from range to score five penalties in total.
The visitors were handed a lifeline fifteen minutes from time when Boris Stankovich was given a straight red card for a dangerous tackle on Dan Allinson.
Irish scored a quick try through replacement Tom Homer but could not finish the job and were left to rue a disappointing defeat.