Arsenal’s Alex Iwobi came off the bench to score the all-important goal for Gernot Rohr's side to help them to their sixth World Cup appearance.
And the former Hull City playmaker is confident that with the mixture of both young and experienced players in the squad they could aim higher than their previous performance where they exited the tournament in the second round.
“We've been to a few World Cups in recent years, and we need to be looking at progressing further - rather than crashing out in the early stages," Olofinjana told BBC Sport.
"I think the country should be looking at perhaps the quarter-finals. It's doable - it's not impossible.
"We have a coach who knows how to bring everybody together, and the boys we've got are hungrier and have a bit of experience - players like (captain) John Mikel Obi, Victor Moses and Ahmed Musa.
"They can bring the younger ones with them so that we do not just to go the tournament to enjoy it but to push ourselves to the next level," he concluded.