George Porter and Jabo Ibehre both went close for Colchester, while at the other end Steve McGinn and David McAllister registered efforts on goal in a drab first half.
Shrewsbury edged the second half, with U's goalkeeper Sam Walker denying both Jon Taylor and McAllister's long-range effort, but the spoils were shared in what was a lacklustre encounter at the Weston Homes Community Stadium.
Turner said: "To be totally safe is a relief, given all of the circumstances of the season.
"There was a lot of energy in our performance and in the second half we got ourselves in some good positions.
"We were a bit too anxious at times and got ourselves offside rather naively on several occasions. But we generally defended well and broke and passed well and it might have been better for us.
"There were some 20-year-olds in our back four and there were other young players in our side too.
"I would imagine it was as young a side that the club has put out for many years.
"But they worked hard and I thought that they did well. The experience will do them good.
"At this stage of the season you need the energy boost that young players can give you and that was the thinking behind it."