James Tavernier's brilliantly taken penalty kick on 19 minutes was enough to give the Light Blues a deserved victory, with a 15th clean sheet of the season also recorded.
Speaking to RangersTV after the final whistle, Gerrard said: "We are very pleased and we are happy with the performance. I thought everyone stood up and was counted today.
"We were put under pressure a little bit towards the end, but all in all I think we were very comfortable.
"There were a lot of questions before the game. We haven't got the best of records here and we knew Kilmarnock were going to ask some questions of us. But the players have answered them.
"They've come here and they have got three big points, they were resilient, they were strong and they put their bodies on the line. They get on the bus very happy and they deserved the three points."
The manager praised James Tavernier after the captain scored his tenth goal of the 2020/21 campaign and his sixth from the penalty spot.
He added: "Superb, that's what Tav is about. He's an attacking full-back and he likes to get numbers in his game. His penalties so far have been outstanding and that's the reason why we put him back on them.
"He needed a little break off them but now he's back and it was a superb penalty. Allan also makes a save at the other end so everyone is contributing in this run and we want to keep it going for as long as we can.
"I couldn't be any more pleased. I've just given them a bit of time off so they can relax and they can rest and get themselves recovered for what's going to be a really extremely tough game away at Benfica.
"But it's a game we should look forward to and we are going to go over there and give it our best shot."
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