Town did not get going on an error-strewn display in their game in hand in League One where former striker Niall Ennis netted after a mistake inside five minutes.
Shrewsbury failed to register a shot on target on a night that left them 15th.
Ricketts said: “It’s an extremely disappointing night. We came into this off the back of a great performance against Bristol City. It started off really badly with us conceding a bad goal – it was unlike us.
“We wrestled the game back for 25 to 30 minutes or so and got into some good situations to score but we didn’t. We didn’t take opportunities to shoot and when we had two v twos, we end up not getting a shot off.
“Their keeper spills one and we don’t capitalise on it, (Aaron) Pierre puts a header just wide of the post. The longer the game went on, we had to gamble to get back into it.
“We have started conceding few goals from set-pieces which is disappointing. The first goal, at least three mistakes in the build up to that one. It was the same with the set-piece.
“We can’t play the game in their half, like we did in the first half, and not test the keeper. There were situations where we could get the shot off and didn’t. We should have worked the keeper.”
Doncaster sealed the win 15 minutes from time on a night to forget for Shrewsbury.
Ricketts, whose side are without a clean sheet in four, added: "I think it was just an off night for us. A lot of people didn't hit the high standards they have on a number of occasions.
"Every three points makes a massive difference. It wasn't a make-or-break for us, there's still a lot of games to go.
"We'd all like to score a lot of goals but it's only the second in 13 or 14 we haven't scored so let's not get carried away. But ultimately we've got to be scoring in the situations we get if we want to push on.
"We didn't hit the heights after giving them a goal. There's no point setting the traps we set if we don't capitalise on them.
"Everyone looks at themselves. We all know it wasn't good enough for when we want to be."