City extended their recent unbeaten run, picking up a third clean sheet on the trot in the process, by playing out a goalless draw with National League side Aldershot at a windy EBB Stadium.
The stalemate ensures City and Aldershot will meet again in a replay at the Coral Windows Stadium in approximately ten days time, with the second round draw set for this Monday night.
Parkinson said: "There were some really blustery conditions out there, and the game was as tough as we thought it would be.
"You look at virtually all the games this weekend between conference sides and league teams - they have been very tight games.
"The TV cameras were here today (Sunday) because they fancied a shock, it was a big crowd for them, and the intensity around us was that little bit greater after what we achieved last season.
"In the first half, I thought we were average at best. We didn't really adapt to the conditions.
"We were a lot better in the second half though. We had a lot more control of the play for long periods.
"We had some decent chances but we weren't able to take them. We came here, however, with the aim of at least making sure we didn't add our name to the list of clubs who had gone out to lower league opposition this weekend, and we've achieved that.
"We would have clearly loved to have won the tie today but we look forward to the replay back up at Valley Parade.
"We have set some high standards recently at home but we'll need to match those standards again in the replay.
"We have a lot of pride in what we achieved in this competition last season and we want to progress again but we'll need to play well in the second game to do so."
Parkinson chose Sunday's tie to hand Billy Clarke his first start in City colours since the Irish attacker injured his knee in the club's first home game of the season back in August.
The City chief added: "I was pleased with Billy - he had a good game.
"it was a difficult game for him to come back into from the start given the conditions but he looked really dangerous. The 'keeper has made a great save from Billy's shot in the second period.
"He is still some percentage off his real top sharpness but we are really pleased with the way he has been progressing recently."