Striker Paul Benson, midfielder Jason Taylor and central defender Michael Hector all impressed on their debuts against Torquay with another new arrival, striker Byron Harrison, coming off the bench late on in the 2-1 win.
"We were excellent," said the Robins boss.
"It took a little bit of time to get into our stride but that's what you get when you bring in a few new faces. I thought we looked strong and organised. We have brought in some good players on top of the ones we already had and they responded in the right way.
"All three lads who started for their debut were excellent. They've all contributed to a good performance and I'm wondering how we made it so hard for ourselves in the last five or six minutes."
Cheltenham dominated throughout but it took until the 33rd minute before defender Keith Lowe headed home a Kaid Mohamed corner to hand them the lead.
Gulls goalkeeper Michael Poke pulled off two excellent saves to keep out long-range efforts from Mohamed and Cheltenham skipper Russell Penn but was helpless to stop Shaun Harrad's low shot five minutes into the second half.
Substitute Daryl Duffy was guilty of missing the chance to make it 3-0 late on when he pounced on a weak back pass only to push his shot wide.
Yates added: "We had lots of chances in the second half. I said to the strikers when they came off the bench that I wanted one of them to score from a back pass because I see back passes go short and we don't chase them.
"I'm not going to moan at Daryl for missing it - he picked the wrong option and should have scored - but he's listened to what I've told him."
Rene Howe grabbed a late consolation, an 88th-minute effort that spun out of the keeper's hands and into the net.