Belles were reduced to 10 players before the hosts scored.
Sunderland’s Rachel Furness played Beth Mead clean through on goal, and she was dragged down outside the box by Belles centre back Leandra Little - who received a straight red card.
Sunderland took control after that with Mead 2, Hayley Sharp and Brooke Chaplen scoring.
Coates admitted a lack of confidence is costing her team, who are winless in the league, although they did beat Sunderland in the Continental Tyres Cup last week.
“We’ve done a lot of work with the girls on confidence with us having a tough start to the season,” she said.
“We had such an incredible high last week. We wanted to continue with that and it feels like the world is against us at the minute.
“The things that are going wrong are controllable which is frustrating.
“What’s more frustrating is that we were conceding goals from set pieces. We still should be able to cope in that situation with 10 players on the pitch.
“I wish the girls took a little bit of responsibility and ownership on that.
“If we could have got our heads around the mental side of being down to ten players, and had the bit of grit and determination we could have stayed in the game a bit longer.”
Doncaster Rovers Belles (4-4-2): Nicola Hobbs; Majumi Pacheco, Leandra Little, Rhiannon Roberts, Rachel Newborough (Marta Bakowska-Mathews 46); Emily Simpkins, Samantha Tierney, Lauren Cresswell (Sue Smith 65), Sophie Barker; Jessica Sigsworth, Carla Humphrey ( Kasia Lipk 35)
Red card: Leandra Little 23
Referee: Helen Connelly
To buy tickets to an FA Women’s Super League match near you click here: http://www.ticketstores.co.uk/fawsl/