But a superb kicking display by full-back Delon Armitage in windy conditions brought the Exiles to within three points late in the second half and Loffreda was relieved to take maximum points.
"The win was important to give this team confidence," he said. "We lost the initiative for 20 minutes but got it back in the second half.
"The players that came in had a big responsibility because this was a must-win game.
"They took their opportunity so we are very happy because the bonus point was very important.
"We dominated territory and had good control. We dominated the second half quite well.
"We changed our lines of attack well and that is one of the main things that I have been trying to work on.
"We talk a lot during the week about my ideas but there is not much time because the next game comes around so quickly. They are getting the idea and they are doing very well."
The Tigers stormed into an early lead when Vesty dived over after good work by All Blacks centre Aaron Mauger.
Samoan winger Sailosi Tagicakibau brought Irish back into the game when he finished off a flowing team move on 24 minutes.
Ian Humphreys and Armitage exchanged penalties before Rabeni latched onto Vesty's grubber kick to again put the Tigers in the driving seat.
Leicester stepped up their forward power after the break and were rewarded through prop Castrogiovanni's score in the 56th minute.
The home side paid for Humphreys' missed conversion as Armitage slotted two penalties to bring the score to 20-17.
With the game on a knife edge it was White's try on 73 minutes which settled it but a proud London Irish director of rugby Brian Smith paid tribute to his side and Samoan centre Seilala Mapusua who broke his hand in a second-half incident.
Smith said: "We are very concerned with Mapusua because he is a such a key player for us.
"He has definitely broken his hand and we are worried that he might have a spiral fracture on the top of his hand.
"He was immense for us. He stepped up to lead the side and he was immense off the pitch as well. We will pray for a speedy recovery.
"At 20-17 I thought we were in this and with the wind in our advantage, the boys kicked very well to get us field position.
"We are looking at the game and wondering how the hell we came away with no points.
"It's disappointing but this is Leicester Tigers, this is Welford Road and it is a particularly difficult place to come and win.
"I am still particularly proud of the performance."