Romanesque architecture was not built during the Roman empire, but dates from the period between 1000 and 1200 A.D. The style is called Romanesque because some elements of it follow Roman architecture, particularly the arches, which are round in the Romanesque style. By contrast the Gothic architects made the arches pointed as the whole philosophy of the Gothic style was based on the idea of reaching towards heaven. The Romanesque buildings also had columns with decorated capitals that were similar to those seen in ancient Rome, which you will not find in the Gothic style.
Romanesque churches are much darker than Gothic ones. One reason for this is the lack of windows. Many Romanesque buildings still had wooden roofs as architects hadn´t perfected building roofs from stone and other materials. Romanesque buildings that had stone roofs had to have very thick walls with few windows in order to support the roof. By the Gothic period, architects had discovered ways of supporting stone roofs and walls that also allowed them to include large windows that allowed light to flood in.
The presence of flying buttresses distinguishes Gothic cathedrals from the Romanesque. Gothic architects wanted more light but had to find a method of holding up a roof while also putting large windows in the walls. The solution was to build an arch that carried the weight of the roof away from the building, so they attached a buttress to the top of the wall where the groin vaults took the weight of the roof; this column carried the weight.
The Gothic architectural philosophy was based on the idea that more light in churches would provide spiritual inspiration. The flying buttresses made it possible for the Gothic architects to introduce more windows and as the style developed the windows themselves became more elaborate. Certainly one way to tell the difference between a Romanesque church and a Gothic cathedral is the presence of a rose window. Although Romanesque churches favored round windows, none have the elaborate "rose" style seen in the great Gothic cathedrals of France.