The Robins pulled a goal back in the 72nd minute after Matt Richards was fouled by Morgan 25 yards from goal and his free-kick deceived goalkeeper Luke McCormick and ended up in the back of the net. But the visitors looked comfortable thereafter.
Home boss Yates admitted his side fell apart after falling behind in the 17th minute.
"I apologise to our supporters for an inept last hour of the game," Yates said. "We started brightly and should have scored a couple, but after they scored we were powder-puff at best.
"I am not going to go over the top but the players know how disappointed I am with that and that they were poor. They'll be in on Sunday to work hard."
Yates said only new loan signing Steven Gillespie emerged with any credit as he considers changes for next week's trip to Accrington.
He added: "Steven looked bright and lively in his first game but we were second best after their first goal and that's not good enough so nobody can be sure of their place now.
"We have been bullied by the two centre forwards and by the two central midfield players and the game became too easy for them.
"You don't have any divine right to win games, no matter who you are playing. We were found wanting and there wasn't a response. "
- Sports & Recreation
- Marvin Morgan
- Conor Hourihane