The Cumbrians were on course to extend their winning streak when Shrewsbury winger Paul Parry raced through to rescue a point for the home side in what was a dramatic finale.
"It's that never-say-die attitude," Kavanagh reflected. "I said to the players that Shrewsbury have conceded late goals. They've drawn six, lost three and won one of their 10 games.
"I felt it was going to be our day, especially when it went to 2-1, but it wasn't to be.
"The dressing room afterwards was pretty quiet. They were euphoric at 2-1 and I just laughed at the end of it and said 'look boys, this is the start of something good hopefully'.
"We are going to have some ups and downs but as long as we learn to lose in the right way, draw in the right way and win in the right way, I mean by the fashion in which we play and the work-rate we give, I'll never have a problem with it."
Kavanagh added he had been delighted with the response from the players since taking over having collected 10 points from a possible 12.
"We work extremely hard through the week," the Irishman said. "We've working longer and harder. We're putting more demands on the group.
"They're buying into it and confidence gives you that, performance levels give you that and I think points on the board give you that."