Suarez received a four-month ban from all football on Thursday for biting Italy defender Giorgio Chiellini in Uruguay's final Group D encounter, which means the Liverpool striker will miss the rest of the FIFA World Cup.
Colombia are Uruguay's next opponents with the two South American nations set to clash in the round of 16 on Saturday at the Maracana.
Ospina is convinced Uruguay have enough quality to overcome Suarez's absence, just as Colombia have advanced without star striker Falcao, who has missed the World Cup with a knee injury.
"All national teams have difficulties," the 25-year-old goalkeeper said.
"We had difficulties but that is why it is down to all members of the team to have the ability and skill to overcome any difficulty."
Colombia coach Jose Pekerman warned his players not to get too caught up in the media coverage of Suarez's ban and was not interested in giving an opinion on the severity of the suspension.
"It is a very delicate issue. It seems to me that our concern is Uruguay and we are working hard to deal with them," Pekerman said.
"Uruguay are highly respected. We knew the possibility of playing them, they are always top-notch. We have to be ready.
"Playing them motivates us. We have huge respect for Uruguay's history, we have to continue moving ahead."
While Colombia (eighth) started the World Cup ranked just one position lower than Uruguay (seventh) by FIFA, Pekerman underlined the Uruguayans' superior pedigree and claimed the pressure is on Oscar Tabarez's side.
Uruguay have won two World Cups in their history, while Colombia have only beaten their CONMEBOL rivals twice in nine matches over the past decade.
"The big teams must prove why they are so big, why they have won things and why they are so valued," Pekerman said.
"In countries such as ours, which hasn't competed at the World Cup for so long, we must show our willingness and ambitions.
"We must know how to compete and we are doing quite well.
"This is a huge test for us. For Colombia this is going to be a demanding test. We will have to show that we can compete."
