"If I had one word to describe Andy's performance, I would say solid. What he did, he did well," said Gaffney.
"Inside centre is a tough position and he needs to learn when to be flat, when to be deep and when to be wide. It is all about experience."
Saracens were indebted to 17 points from fly-half Glen Jackson, and Gaffney added: "His all-round performance was superb. Thank heavens he is durable, because we have got no cover at fly-half at the moment."
In a frantic finish to the game, Leicester hooker James Buckland crossed under the posts, but referee Roy Maybank ruled that he had not grounded the ball and Saracens held out for a deserved victory.
But Leicester head coach Pat Howard said: "I spoke to Saracens' Paul Gustard, who is a good friend of mine, and he said that James scored but the referee could not see it.
"There were some big decisions in the last 10 minutes and we made lots of small mistakes.
"It took a long time for us to get into the game and we had trouble with our line-out in the first half.
"But I am proud of the performance of the guys, especially as we had 13 players missing who have gone off to all parts to play for their countries."
Bath slipped into the bottom three after crashing 47-18 against Wasps, who moved third, just one point behind leaders Gloucester and second-placed Bristol.
"The players are upset with this performance," said Bath's acting head coach Steve Meehan, who could have England centre Olly Barkley back from injury to face Bristol next Saturday.
"Missed tackles against such a dangerous side as Wasps just kill you, and if you don't kick well, sides will just counter-attack you."
Ex-Leeds Rhinos rugby league star Chev Walker made his Bath first-team debut off the bench, but the visitors were swamped as wing Edd Thrower scored four of Wasps' seven tries.
"Thrower has been playing well in the second team, and he took his opportunity. He did the simple things well," said Wasps rugby director Ian McGeechan.
"The way we defended in the first 10 minutes set us into the game, and the first opportunity we got, we scored."