Last season's beaten finalists lost their opening Pool Six game against Leinster but put that behind them to power to a bonus point win in Loffreda's first game in charge at Welford Road.
Andy Goode's 14 point haul made him Leicester's leading scorer in the competition, while Geordan Murphy equalled Leon Lloyd's club record of 19 tries in the Heineken Cup.
And captain Martin Corry capped his 250th appearance with the fifth try in injury time.
Leicester face crunch back-to-back games against Toulouse next month and confidence will be high after today's win.
Loffreda said: "It was very important for us to win and we played a much more intelligent game.
"We played practically and a lot better in defence. They are the two things we have been working on."
Leicester were 17-0 ahead by the opening quarter and Loffreda said: "Edinburgh can score points when they have possession, but they never got the ball. In the last 20 minutes of the game they had the ball, but for 70% of the game we had the ball.
"We wanted to play in their half, we did that well and I'm pleased.
"After 60 minutes I think we lost a bit of consistency. We could have been more dominant, but there were changes and that contributed to the loss of momentum."
Edinburgh coach Andy Robinson wasn't happy with referee Romain Poite and his decision to sin-bin Craig Hamilton and Allan Jacobsen in the second half.
Robinson said: "We were physically dominated.
"We were bullied the whole game and I thought the referee got bullied as well.
"I didn't think we were allowed to scrummage the way we did last week when we put Toulouse under pressure.
"Jacobson had a storming game last week and was sin-binned today. It's all about interpretation."
Robinson knew the writing was on the wall from the opening minute when Leicester crossed for two tries.
Robinson said: "We knew the backlash was coming and we couldn't withstand it well enough in the first 20 minutes. You have to start well here. We knew what was coming and fair play to Leicester because there was instant pressure for us every time we had the ball.
"Leicester had been beating themselves up all week and that's how they responded.
"We have to respond in the same way."