The 44-year-old was sacked in January but returned to the helm on March 3 with no upturn in results in his absence.
Last season's Serie B champions have taken four points from the two games since Di Francesco's comeback, drawing at fellow strugglers Bologna before beating bottom side Catania.
Now in 19th place, Sassuolo travel to Udinese this weekend and Gazzola wants to keep the recently found momentum going.
"Against Bologna and Catania we had been given some direction under Di Francesco," he said.
"The enthusiasm brought by the coach was crucial because before that training was very serene.
"We had not won in a long, long time and the victory against Catania served us well from all points of view. Now though we are already thinking about the next game to give continuity to what we are doing.
"We now play Udinese and they have had excellent results in Serie A for many years and have strong individual players, it will not be easy at all but we are aware of our strengths and we want to take the points being at home."
Udinese are 14th in the table and go into the game having run second-placed Roma close in a 3-2 defeat on Monday.
Coach Francesco Guidolin was pleased with the effort earlier in the week but has urged his players to now turn their attention to the Sassuolo clash.
"We had the right attitude throughout the whole game against Roma," he said.
"I thought we were naive for some of it and we have to improve that aspect of our game - we have to look to the Sassuolo match.
"It is going to be a very important one for us, we need to prepare well because they are a good team who can cause us problems."