After going ahead early-on through Ryan Jack, Accies leveled but Ryan Kent stuck at the end of both halves to ensure Gers made it six wins on the bounce in all competitions.
The manager was still asking for more, however, when he spoke with RangersTV in South Lanarkshire at full-time.
He explained: “We have certainly played better. I thought we were good in patches and we obviously scored three decent goals, so it is an away win and there are a lot of positives to take from the game.
“But, on the back of an international break, and people being all over the place and the preparation being different, we will certainly take a 3-1 win on the road.”
Kent’s first goal, in particular, was top-class, with the manager continuing: “It is a terrific strike on his left side, and that is what he is capable of and that is the reason why we spent all that money on him.
“I thought Jacko [Ryan Jack] was magnificent to get another goal too, but his all-round performance was very strong again.
“So I think you saw two sides of us today – at times you saw our quality but at times, I wasn’t happy with certain things about us defensively – I think we need to be better than that.
“We have quality in our team and I thought we could have scored more goals today. Hamilton did well to stay in the game, but we were much the better team and there was only one team really trying to play the right way and trying to create and score goals.
“Unfortunately, we just couldn’t do it quick enough today to relax and enjoy the game.”
Gerrard included 17 year-old Kai Kennedy in his squad today as the 19th man, with the gaffer insisting it was well deserved for how he has performed in training.
He added: “That was nothing to do with being young, if you like. Kai has trained with us all week – he got a cameo against Leicester and earned the chance to come and train with the first-team and travel and warm-up with us today.
“It will be a good experience for him as he is certainly a talent. There is a lot of work to do with him but we certainly see a bright future for him.”