Dorking, who were relegated from the National League last season went ahead when Jimmy Muitt’s 15th-minute goal quietened the crowd of 2,676.
But City striker Tyler Harvey levelled the scores after 31 minutes, only for Charlie Carter to get what proved to be a winner three minutes into the second half.
“I’ve got mixed emotions,” said former York City and Macclesfield Town boss Askey, who took over at Truro in the summer after Paul Wotton left to manage Torquay United.
“It was great to see so many people here and a good atmosphere, and once we got to grips with Dorking we started to cause them one or two problems.
“I’m disappointed in the first goal that I thought was a blatant foul, but it happens and we did well to get ourselves back in the game.
“We we’re in a good position and you think ‘we’ll start getting them rattled’ and then we concede from a corner – people losing their men and not reacting to the second ball.
“But I can’t ask any more of the players, I thought the players worked really hard and they’re a team that are fancied to go straight back up the huge budget, so I thought our players did well.”