After going down to a Mickael Pote strike in under two minutes, the Black Stars fought back to end the first half 2-1 up courtesy of goals from captain Andre Ayew and his brother Jordan Ayew.
John Boye's sending off for a second bookable offence on 54 minutes, however, gave Benin a numerical advantage. The Squirrels made the most of the situation as they turned on the heat on Ghana, leading to a Pote equaliser in the 63rd minute.
"It was a good game," Appiah said at the post-match conference.
"We didn't concentrate in the first half.
"In the second half, it was hard to play with 10 players. A draw is reasonable.
"I didn't lose hope in my team. Wait for us in the next game."
The Black Stars next face defending champions Cameroon on Saturday before squaring off against Guinea-Bissau in their last group game on July 2.