With the scores still level after 120 minutes, penalties were required to decide who would face Sweden in the quarter finals, as England banished their demons to win their first World Cup penalty shootout, although Pekerman was far from complementary of Gareth Southgate's side post-match.
Captain Kane, whose second-half penalty put England 1-0 up before Yerry Mina's injury-time equaliser, believes England came of age last night.
David Ospina dived superbly to his left to repel Jordan Henderson's third penalty for England, but Manuel Uribe hit the crossbar before Jordan Pickford saved from Carlos Bacca.
Southgate's side has struggled to break down teams with a similar approach - needing an added-time victor to beat Tunisia in their opening game and then only scoring courtesy of a Harry Kane penalty in the meeting with Colombia.
If England get past Sweden they face a potential semi-final against hosts Russian Federation or Croatia for their first appearance in a final since winning the World Cup for the only time in 1966.
Tuesday's match marked the sixth clash between Colombia and England, with England victorious on three previous occasions and drawing with Colombia twice.
"We've not got a good record against them, I think we've always underestimated them".
"We had total belief in what we were doing, right through to the end".
Southgate has challenged his players to write their own history after England's poor recent results at finals. The country's only shootout success came earlier at Euro '96.
"Tonight was a classic example".
"Today is a special moment for this team".
Jordan Pickford's magnificent save.
"It was a top class save and I was surprised he could reach it given his height", he said with a grin.
He posted this message on social media, saying: 'I've just experienced the most fantastic 24 hours watching my brothers come through a tough game both mentally and physically.
"His athleticism around the goal is excellent and he executed the plan in the penalty shootout".
"The best player was Mina", said lawyer Adriana Palma, 33. I don't care if I'm not the biggest keeper in the world. "I hope it will give belief to generations of players that follow, because they can see what is possible in life". Now coach Gareth Southgate will need guide his young players against an experienced Colombia squad capable of dominating both sides of the ball.
"It's like a scene from "MASH" in the dressing room". When there are so, so many fouls and interruptions I think that's not good.
"We know the size of the task and we know the difficulty of this task".
Gareth Southgate made as many as seven changes in the 1-0 loss to Belgium and may recall numerous rested players back in the starting eleven.
"It has been very uncomfortable to play this match knowing that feeling was in the air about refereeing decisions".