Captain David Weir was satisfied after Rangers overcame a below-par performance to snatch victory at Hamilton.
And manager Walter Smith was delighted to leave with the points after being "stretched to the limit".
Nacho Novo's late goal settled matters but Hamilton had plenty of scoring chances against a Rangers side which was missing several key players.
Weir told ESPN: "It's always tough, any time you go away in the SPL it's a tough game. We never played well enough in the first half but I thought in the second half we improved and I'm delighted for Nacho, getting the goal.
"The result is most important but you want to have the performance and the result. There's things we didn't do well enough today but the fact we've won the game is the ultimate aim.
"You don't get anything easy coming to places like this, you've got to work hard and do the dirty jobs.''
Hamilton had held Rangers to a 3-3 draw in the Scottish Cup last Sunday and could easily have come out of the game with another positive result.
Rangers manager Walter Smith praised his side after admitting they were down to the bare bones for the clash.
Smith was not even able to fill the bench, with several youngsters named as substitutes to make up the numbers as so many first-team regulars were unavailable.
He said: "It was an opportunity for them, there is no doubt about that. But putting them in for the first time and the number of changes we had to make made it awkward for the lads.
"It was the same with Maurice Edu and Kevin Thomson. I was just delighted that we got the goal considering we were down to the bare minimum of players.
"We didn't play well at all in the first half. Accies were the better side and we struggled to get to grips with them in all areas of the pitch.
"In the second half, we picked up a bit, played better and imposed ourselves on the game more and I was delighted that we got that late goal.''
Rangers face Hamilton for a third consecutive time in Tuesday's Active Nation Scottish Cup replay at Ibrox after being held to a 3-3 draw last Sunday. And Smith does not expect his options to improve greatly for that game.
He said: "Kenny Miller will be back from suspension but I don't think anyone else will be back from injury. DaMarcus Beasley and Steven Naismith might be okay for next weekend but we will wait and see on both of them.''
Hamilton manager Billy Reid clearly felt his side deserved something from today's game and admitted afterwards: "It was a sore one. The players are downbeat after the performance they put in.
"We were the better side in the first half, we created chances and we should have been ahead at half-time.
"We knew they would come at us in the second half and they scored a late goal. On another day, we might have got the break and the ball would have gone in for us.''
Looking ahead to the cup tie, he added: "It's a different arena and Rangers will be at home. The most important thing is that we continue to make progress at this club and, against the Old Firm, we are making progress.''