Ghana went through after beating South Africa 2-1 and will meet the Group D runners-up in the quarter-finals on Sunday evening.
"With this team we can take on anyone in this competition," he said.
Algeria qualified as Group C runners-up and Trainer Christian Gourcuff said: "It was not easy to get out of this group."Gyan scored Ghana's late champion in their second game against Algeria which ultimately helped them finish topmost of the table on head-to-head record.
He added: "I have played at five cups of nations, but this group was the toughest.
"We were very strong intellectually, even after granting the first goal. We reserved trusting and fought to the end knowing that we could win.
Ghana manager Avram Grant said: "We justify it because South Africa were not better than us.
"We have finished first in the group of death, which is not bad. After losing the first match we showed great attitude in the second and continued along the same lines today.
"We started the match very well with two or three good chances. We had the match in our hands. I am very happy that the players exhibited, just as in their last match, a good spirit and good attitude."
Gourcuff said that Algeria's 2-0 victory over Senegal had been hard-earned by his players.
"It was an extremely difficult game physically," he said. "The ball was almost always in the air, which is not an advantage for us.
"We needed lots of discipline strategically and our technique and speed on the break assisted us win."
"We are two completely different teams in terms of our tactic. We have lots of small technical players and Senegal are more direct and physical."
"But our technical quality shone through on the counter-attack in specific."