The Ibrox side were worthy victors as they defeated St Mirren 3-1 in their first league match courtesy of Lee Wallace’s early double and a late clincher from substitute Dean Shiels.
Once again, as they did in cup ties against Hibernian and Peterhead, they finished the match strongly as their fitness shone through.
Despite dominating for large spells of the game, however, the Championship title favourites were fortunate not to find themselves pegged back with just over half an hour left.
St Mirren were awarded a penalty as they trailed 2-1 and Steven Thompson missed a glorious chance to level as he put it over the bar.
Rangers kicked on and secured all three points late on but only after squandering a number of good opportunities and Warburton realised that.
The former Brentford boss said: “We have to recognise we need to be more clinical. (In) the second half we had chance after chance but 2-1 is a dangerous scoreline.
“A couple of times we were close and they broke on us. It’s about keeping discipline with pitch geography. We got away with it when they missed a penalty.
“But overall I thought we were the better side. Lee Wallace was outstanding for us. It was a first-class performance.
“We have to take our chances though. We only met six weeks ago so we are far from the finished article.
“There’s a lot more to come from this group of players. With their work ethic and quality, I think we will get better and better.”
St Mirren boss Ian Murray admitted his side had been blown away by the ferocious noise created by pumped-up home fans.
A crowd of 49,216 gathered at Ibrox and created an excellent atmosphere as the Championship campaign got underway.
Murray said: “I think the crowd and the occasion got to the young guys. They have not played in this environment before and you could see that but their reaction to the second goal was superb
“It was a huge blow when we missed the penalty because we felt we still hadn’t played to our potential at that point, so to get to 2-2 would have been great.”