Enrique's comments come after rumours surfaced that he told Busquets to provoke the Celta Vigo players.
The incident occurred towards the closing stages of the match when Celta Vigo's Fabian Orellana was given his marching orders in the 88th minute after hurling part of the turf at Busquets as the midfielder took a prolonged amount of time to take a free-kick. As Busquets was also booked, he will miss Barcelona's La Liga match against Almeria on Wednesday.
"We never ask our players to force a yellow card," Enrique said during a press conference. "I didn't ask him to force it, but rather I told him to be careful about getting booked."
However, Celta Vigo midfielder Pablo Hernandez was disgusted by Busquets' behaviour towards the end of the match.
"How can he have seven fakes and take more than a minute for a free kick?" Hernandez said. "It hurts because he is mocking us. We are colleagues and he should show us respect."
Hernandez has also called on the team's administration to launch a formal complaint about the incident.
"It is obvious, anyone can watch the replay. You could just see it. The small details make a big difference," he said. "Barcelona had the advantage after that. There are others who need to speak on our behalf because we need to focus on playing. The club's leadership will know what to do and how to have an impact."