The four-time champions secured a place in the final of the Africa Cup of Nations, with Jordan Ayew, Mubarak Wakaso and Andre Ayew on target in a dominant victory against the host nation.
But, following Ghana's first two goals as half-time approached, the mood turned in the stands at the Estadio de Malabo and sections of the crowd began to throw objects.
Ghana's players were shielded by police as the left the field at the interval and the situation deteriorated to the extent that there was a half-hour delay before the closing stages of the match could be completed.
Both teams remained on the field as confusion reigned during the stoppage, brought about when Ghana supporters gathered behind one of the goals to avoid being hit by missiles.
"It's the first time I've played games in this tournament," Grant told reporters after the game.
"I didn't know what was happening, we saw some incidents of violence.
"I could not say I wasn't concerned but I wanted to keep the safety of my players - it was very important for me."
Reacting to events on the field, Grant praised his team's composure throughout the contest and credited them for surpassing pre-tournament expectations elsewhere.
"We tried to hold the ball, control the game and find the solution to score the goals," he said.
"I think we did it well, it was not an easy game. Equatorial Guinea played well in the first half in a tactical way to stop us playing."
The former Chelsea manager added: "I don't think anybody counted on us before the tournament, nobody thought that we would do something good.
"Everyone was picking the Ivory Coast, Cameroon, Algeria or others but I said to the players that it doesn't matter what people say. It matters what we do on the pitch.
"I think from Ghana you've seen good quality of football, a lot of character - you can see this is a team for the present and for the future."
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