"We're all pleased to get the first game over," said Garvey. "We always knew Birmingham were going to be a potential banana skin, especially it being a local derby, so it was good to get out there and get a positive result.
"We scored six tries after a slow start; we only got two in the first half and probably should have had more. But in the second we showed we have got the desire to keep going and get that first bonus point.
"On a personal level, it's nice to get off the mark - it always is. I had a bit of a drought last year, but I got a try in pre-season and it was good to get one today and start the ball rolling.
"A lot of the boys showed real potential and if we stick together and keep getting better we can score a lot of tries."
After the game, Head Coach Richard Hill insisted the best was still to come from his team and winger Garvey echoed his comments as Warriors prepare for a trip to Plymouth Albion next weekend.
"I would totally agree with him - that is a fair reflection of how we played," added Garvey.
"It was good that we didn't let them score a try. But they broke our line too much and that is not acceptable with the calibre of players we have got.
"We need to keep working on the defensive system and get that right; hopefully there will be improvement in the next game.
"Plymouth is not an easy place to go, they maul a lot and slow the game down so we have got to go down there and play a high tempo game to try and come away with a good result."