The home side controlled the ball for much of the game and ultimately won the match thanks to strikes from Danny Ings and Emiliano Buendía.
“I certainly believe that our performance over the course of the 90 minutes deserved the outcome we got," Gerrard said.
“It was much different to last week: more quality, everyone was tuned in and contributed to an important win.
“The conditions were extremely hard today and we had to give a lot to the game. We have to check on a few injuries and knocks we've got.
“I'm hoping that's not going to dampen the feeling we've got because it was important that we bounced back today and important that we gave our supporters a better level of performance. Our players have delivered."
Getting off the mark was important for Gerrard and his team, but the head coach knows there are areas to work on as they look to build upon a first win of the season.
He said: “We controlled large parts of the game, we passed the ball extremely well, our positioning was much better. Our regain and go to go and execute was fantastic and we got two goals on the back of that.
“We still need to learn, we still need to be less naïve and manage games better. At 2-0, we've put ourselves under extreme pressure by not defending for their goal very well.
“We've still got bits and bobs to learn off but our first game at home, when the fans are in that noise on the back of last week, it's a big win for us."