Barry Conlon put Grimsby ahead in the 55th minute after Graham Coughlan had headed a shot from James Hunt off the line, but Shrewsbury responded when Steve Leslie crossed the ball for Ben Davies, who scored his 13th of the season from a tight angle soon after.
Grimsby now sit just one point above the drop zone following Chester's win at Notts County, but Newell said: "I can't fault my players. In the last two or three games we've shown good steel and a bit of quality. I'd have settled for a point beforehand against a side who've won 14 home games.
"Other results haven't gone our way. On another day we may have got three points. Shrewsbury started better, but overall we created enough chances, especially in the second half."