Kwesi Appiah's side fell behind in the 40th minute in the Kasarani Stadium after Nicholas Opoku's own goal, and even though the hosts were reduced to 10 men following Joash Onyango's sending off, they weren't able to equalise.
The victory was Kenya's first competitive triumph over the Black Stars and only their second win against Ghana since a friendly victory in 2003.
It's a defeat that must prompt improvement for the West African giants, according to returning Asamoah.
"We played so well and had a lot of chances [with] which we could have won the game," he told Joy FM, "but we couldn't make it.
"This is a wakeup call for us, and [we must] know that now in football there is no country you can beat easily.
"The outcome of the game will also motivate us to improve going into our next game."
The draw leaves Ghana with three points from their opening two fixtures, having begun their campaign with a 5-0 demolition of Ethiopia in June 2017.
Despite returning to the Black Stars fold for the first time since 2014, Asamoah was overlooked by Appiah for Ghana's starting XI before being given a late cameo.
The West Africans will continue their campaign with a double-header against Sierra Leone in October.