Despite a scoreless first half it was Coventry who came closest to opening the scoring early on as defender Liam Kitching rattled the crossbar from a corner with a headed effort.
The hosts took the lead just before the hour mark through Thomas-Asante when his shot looped over U’s keeper Matt Ingram into the back of the net.
Thomas-Asante came close to doubling the lead in the 75th minute with a header that forced an impressive save from Ingram, who followed it up with an strong palm to deny Ben Sheaf from range minutes later.
After a successful run in the FA Cup last campaign that culminated in a semi-final appearance, Mark Robins’ side will be hoping for similar joy in the EFL Cup this campaign.