One man came in for particular praise and that was Academy graduate Glenn Middleton who made his debut as a late substitute and Gerrard was certainly pleased with his short contribution.
He added: "Am I confident I can break into the side?"
Scotland Under-21 worldwide Middleton joined Rangers from English Championship club Norwich City in January but has had to wait until the summer arrival of Gerrard to make his first-team bow.
He said: "We were satisfied with the win and the clean sheet".
"I think there are a lot of positives to take from the game. but one concern would be that we didn't win the game a lot more comfortably and put the whole tie to bed tonight".
"I felt we should have had the game done by the time we got the second goal with the chances we created".
"It's about taking it day by day, that's the manager's message to everyone and me personally - just do what I can every day to show what I'm capable of".
Gerrard's first away game will be the return fixture on Tuesday.
They did grab the second their dominance deserved two minutes into stoppage time after Ron Broja brought down Murphy in the area, Tavernier coolly slotting the resulting spot-kick home to cap a memorable night for Gerrard.
Middleton admitted he did not expect to play a part in Gerrard's managerial bow but hopes to continue impressing the former Liverpool skipper. "Not many people are sure what to expect when a new manager comes into a club, no matter who it is".
"It's our first competitive game". It was a really good result for the team, although obviously it wasn't the flawless performance. "He has a part to play and it is important now he enjoys tonight and then gets himself ready for the next game". With the second leg cycling round fast, he will want more from them to ensure we quickly put the tie beyond the opposition and don't set ourselves up for a nervy end.