Victory would have seen Jimmy Dack's men move above Plymouth Argyle into seventh spot, but they were unable to see off a Cheltenham side battling to stay in the Football League.
It could have worse for the Welsh side, who had to come from behind to secure a point after a defensive mix-up gifted Wes Burns an opening goal after only 13 minutes at Rodney Parade.
Miles Storey equalised by heading home Ryan Jackson's inviting cross seven minutes before half-time, but Newport were unable to force a winner and are now without a win in three matches.
A point for Cheltenham leaves them two points better off than second-bottom Tranmere Rovers, who travel to Northampton Town on Saturday.
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