The Giallorossi cruised into the quarter-finals of a competition they have already won nine times thanks to first-half goals from Miralem Pjanic and Osvaldo, with Mattia Destro adding a third after the break.
But Osvaldo allowed Atalanta to take control of the latter stages of the second half after picking up a red card for throwing a careless elbow at Carlos Matheu.
Roma survived a late onslaught to move one step closer to claiming a first Coppa since 2008, but Zeman was left unimpressed with Osvaldo's contribution.
The Czech tactician told La Repubblica: "I have no idea why he got himself sent off and when a player deprives the team of a man, it's not good.
"We let Atalanta take the initiative in the second half and, despite the result, we suffered from being a man down. But I'm happy with the result and how we got there. We contested a good game.
"We succeeded in doing what we set out to do at the beginning. We used a lot of players who haven't featured much and they all played pretty well.
"I hope that we can get even better and we are convinced of our own ability. We have everything to play for in the next round and we can keep pushing on in the league as well."
Atalanta boss Stefano Colantuono was similarly disappointed with the efforts of one of his own, with goalkeeper Andrea Consigli failing to sweep up easy balls for Roma's first two goals.
"Roma have improved and they've definitely shown that over the last couple of games," he told La Repubblica. "But we facilitated it for them tonight [Tuesday].
"We should have done more but Roma's first two goals complicated the game. They have some great players and they can force you to play badly, because if you're chasing the game everything becomes more difficult.
"We made the most of our numerical superiority after the break but we weren't crafty enough. It's a shame because I thought we could go further in the cup."