Relegation-haunted Rovers turned in one of their best performances under Gary McSheffrey as they offered much more attacking threat.
But Bolton’s superior finishing condemned Doncaster to a damaging 2-1 defeat which left them on the brink of relegation to League Two.
“It was a very good win for us,” said Evatt, a childhood friend of McSheffrey’s.
“I thought they were excellent. I thought they were well prepared.
“It was more or less on the line for them today so they chucked everything at it and it was a really good and spirited performance from them.
"We had to ride the storm a little bit in the second half but we’ve got some very good forward players and they’ve come up with the goods for us, but I thought it was a good game of football.
“I thought it was entertaining and a bit of needle and spice but there’s nothing wrong with that.
"We all want to win and they want to win and credit to them. I thought they performed very well.”
Jon Dadi Bodvarsson broke clear to square for Amadou Bakayoko to break the deadlock for the visitors shortly after the restart.
Mipo Odubeko fired home an equaliser just moments after coming off the bench but virtually straight from the kick off former Rovers winger Kieran Sadlier volleyed home Dapo Afolayan’s ball into the box to seal the points for Bolton.
“We’d highlighted from our analysis work that they were susceptible from crosses in particular and we’ve scored from two crosses and probably could have scored a few more from crosses first half in particular,” said Evatt.
“But they were two very well taken goals.
"I’m pleased because I think it was a challenging game today. I think they threw so much at us and we had to dig in and fight and scrap. I thought our attitude and professionalism was excellent.”