Garner, 28, joined Rangers in August from Preston for a reported £1.8million fee and has so far managed three goals in nine Premiership appearances.
Former Rangers winger and Scotland international Neil McCann has criticised Garner recently and Warburton has now responded, stating he felt McCann took a "cheap shot" at his summer recruit.
The Rangers manager says Garner needs more time to adapt and remains confident the forward will be a success in Glasgow.
Warburton compared the start of Garner's Rangers career to that of Andre Gray's at former club Brentford, pointing out the forward initially struggled to settle at Griffin Park before establishing himself as a key man and earning a big-money move to Burnley.
"If you want my honest opinion I’m disappointed when ex-players take cheap shots. Everyone is entitled to their opinion," Warburton told the Evening Times.
“But to look at it on such a micro level? Look at the bigger picture. How long has Joe been here? How many games has he played?
“I saw recently in a presentation that Andre Gray scored two goals in 10. By his own admission Andre, who I have so much respect for, he wasn’t playing the best.
“Had Scott Hogan not been injured he might not have played a few games. But he stayed and scored five in the next 10 games. Then four in the next 10. He ended up scoring 16 and leaving for £7million.
“But he scored two in 10 to begin with. At Brentford the focus was not quite so intense. Eventually he grew into a £30million striker, a magnificent player.
“Joe has been here such a short period of time and I was disappointed by cheap shots of that nature.”