Beaten 2-1 by Japan in their opening Group H fixture, Colombia needed to beat Poland to keep alive their hopes of a top two finish and strikes from Yerry Mina, Radamel Falcao and Juan Cuadrado saw them finish the second round of match in third place - one point behind joint-leaders Japan and Senegal.
A victory over Senegal in their final match of the group stages on Thursday would secure their place in the last 16.
Pekerman said: “This victory will make us stronger. Our fitness levels are improving and we stayed true to that style from start to finish against Poland.
“We won’t go over-board – mentally we are in a good place but we need to improve because we are ambitious and want to continue in this World Cup as we’d hoped. We are going to go forward with faith.”
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