Tries from Jamie George, Duncan Taylor, Joe Maddock and Andy Saull steered Saracens to five points and the game was over at half-time as the home side went in 27-0 in front at Bedford's Goldington Road, their 11th different venue of the season.
Gustard said: "It was a brilliant first half in which our youngsters really came to the fore. Ben Ransom was instrumental in that first half and Duncan Taylor, the local boy come good, did really well as well.
"Saracens often get criticised for not playing attacking rugby but we showed we do play attacking rugby when the conditions allow.
"Knowing Leicester, their culture and their coaches and Cockers (Richard Cockerill) being a vociferous young character at the best of times we expected a response and unfortunately for us we allowed them to come back into the game a little bit.
"We slipped off a few tackles and our mistakes helped them get back in it. John (Smit) is not a bad sub and at that time I felt it was important to get his experience on there to shore things up despite how well Jamie George was playing."
Leicester director of rugby Richard Cockerill was not happy with his side's first-half display or the sin-binning of Lucas Guillaume after just nine minutes.
"At 13-0 with the slope against you it was not too bad, especially with the sin-binning which was bizarre," he said. "It was for us entering in at the side when we have the ball - it is clearly a new directive from the IRB. That was a little bit harsh.
"You could cope with that, but then they get an intercept and then you turn it over and it is 27-0 and it is an uphill task.
"In the second half we got back in it, it is a hard slope to play up and we should have realised that sooner in the first half, but that's life. We came away with some pride in the second half, but at 27-0 you are never going to win any games.
"The officiating was inconsistent for both sides, but that is all right we weren't good enough to win."
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