The England international was making his first return to action since hobbling off in the Guinness Premiership game away to Newcastle Falcons back on January 7.
"It was good to be back, and there was no reaction from the injury," said Goode, who successfully kicked five prenalties from five attempts and added a conversion.
"It was a tough game, we kept scoring but we couldn't quite break the shackles. In the second half we put a bit of pace in the game and started to enjoy it. I thought we were in control without ever really seeing them off. But, after the Northampton game the previous week, a win is a win."
Goode and his Tigers team-mates will now be looking to build on that with a trip to Kingsholm to face high-flying Gloucester on Sunday afternoon.
"It is an important time in the league but we have seen anyone can beat anyone - Northampton came and beat us, which was a shock to everyone, probably including themselves," said Goode. "Teams at the bottom are fighting for their lives, teams in the middle are fighting for European places and the teams at the top will probably lose games between now and the end of the season. It is a big game, Gloucester are going well this season."
Goode faces competition for the Tigers No.10 spot from Paul Burke and Ian Humphreys, but with all three having their chances in the team, head coach Pat Howard wants to see them push each other for selection.
"I was glad to see Andy kicked his goals," Howard said after last Saturday's win over Harlequins. "You want guys to put down that sort of performance and say 'This is my position'. I thought Andy made a big statement with his performance and it is up to him to keep applying that sort of pressure on the other 10s."