The Robins nearly went ahead in the 12th minute when Billy Jones' free-kick found Russ Penn, whose effort was saved by Stuart Nelson, with the Gills goalkeeper also getting down to keep out Kaid Mohamed's low drive.
With 15 minutes remaining substitute Deon Burton met Matt Fish's cross but his diving header flew just wide to ensure Cheltenham left with a point Yates felt was well deserved.
"They have scored a lot of goals four or five times already this season and it was important we didn't give them anything to hang on to," Yates said. "We have shown I have a team of men. We didn't want to come here and say it's great to be involved in a top of the table clash and get beat.
"We talked about having the calmness to defend for our lives and in an organised fashion, and although we didn't manage that in the second half I won't be moaning at them. Teams have come here and been destroyed so we did really well, and a point is a good result."
Gills counterpart and ex-Town boss Martin Allen added: "They (Cheltenham) were so unlucky not to win at Wembley and to be honest they should be playing in the division above now. I expect them to be promoted but it is our job to stay above them, and we will."