I recently answered a similar question here in some detail, which you might find useful and/or interesting.

In summary:

There wasn't much sense of responsibility on the part of the Romans. Some Christian traditions did partly blame (or at least punish) the individual Romans involved, such as the Roman soldier who pierced Jesus with a spear while on the cross, but, all things considered, by the 4th century Early Christian beliefs were already formed in such a way that they did not blame the Roman Empire or the Roman Emperor for the death of Jesus. Rather, they blamed the unbelieving, Jewish crowd/priests. Furthermore, the early Christians had a tendency to see their (or their ancestors) conversion to Christianity as being (spiritually) reborn and as such most Christians differentiated between the pagan and Christian Roman Empire.