Following a barren draw after normal time, the Scientific Soccer Lads held their nerves to emerge 4-2 victors on penalties at the El-Wak Stadium in Accra.
"It was a good game but we made some mistakes which we could have been avoided, but we will work on it before our next game," Osei-Fosu said.
"We suffered in the early stages but once we got into our stride in the second half, I think we controlled the game well.
"That was the reason why they had to change their strikers because my defenders subdued them.
"We have been resilient in defence this season and that has been the key to our game this season.
"The statistics show that we are one of the teams that have conceded fewer goals this season."
Liberty, by the result, have progressed to the round of 32.
The Dansoman-based side are seeking to win the cup competition for the first time ever.
Saturday's game makes it six consecutive stalemates for Liberty in all competitions, having successively drawn five in the Premier League.
Osei-Fosu has so far been the stand-in head coach this season in the absence of Sellas Tetteh.