A brace from top scorer Brett Pitman, an early penalty and an unstoppable 25-yard shot, was added to by an own goal from Jermaine Grandison as the Cherries equalled a club record of seven successive Football League victories.
The result leaves the Shrews still anxiously looking over their shoulder at the League One relegation zone.
"It was difficult watching," admitted Turner. "Bournemouth are a team in form and they're right up there for a reason, and we're a side near the bottom of the table for a reason.
"That was evident but what was annoying was they out worked us.
"They've got some very good players, some excellent players by these standards, and they're well organised. The only way we could really get a result was to out-work them and we didn't. We came off second best in that as well."
Shrewsbury are six points clear of the relegation zone but Turner insists there is still work to do.
"We've got three massive games left and we need one win," he added. "We have to regroup. It's no good getting carried away because of this defeat.
"You have to hold your hands up as we've been beaten by a better side. Our defending was a bit shambolic at times and we contributed to our downfall with the penalty so early, but we've got to be prepared to be ready for Colchester next Saturday."
- Sports & Recreation
- Jermaine Grandison