Hot-shot Jamie Cureton scored his 13th of the season, a goal which proved enough to give the Grecians their first win at Valley Parade for 29 years.
The 37-year-old striker, who played in the same Reading team as Parkinson, rounded off a superbly worked goal two minutes before half-time, hooking the ball home after Craig Woodman's cross to the far post had been headed back into the goalmouth by Matt Oakley.
"We just lacked spark in the first half and enough skill to go past someone," Parkinson said. "We have injury problems and we have played a lot of matches, but we had players out there who didn't play in our FA Cup match against Northampton in midweek.
"I just felt the players we had out there didn't suit the opposition. We could have done better and played with more desire than we did in the first half.
"We looked brighter and sharper in the second half and we thought it was a penalty when Nahki Wells was fouled. Garry Thompson had a great chance and James Hanson's header went over the bar - those chances have got to go in. If one of those goes in then the game changes. When you have been beaten you want another game to come quickly and we will be ready for Plymouth at home on Tuesday."