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The result sees second-placed Liverpool close the gap to the Premier League leaders Manchester City to one point.
"Thank God the game has two halves," Klopp told BBC Sport after the game, "We didn't play particularly well in the first half. They made it uncomfortable but we didn't get in behind the last line. We didn't have enough movement.
"We weren't quick enough. We passed the ball into the area they had nine players. Second half we were much more direct and caused them much more problems. The goals were wonderful."
Both teams failed to create many clear-cut chances in the first half as Everton set up to frustrate Liverpool with a defensive set up.
The biggest flashpoint came just before the break as both sets of players clashed after Liverpool failed to put the ball out after Richarlison went down injured.
Liverpool finally broke the deadlock after the hour mark when Robertson headed home from Mohamed Salah's floated cross.
With five minutes remaining, substitutes Luis Diaz and Origi combined to double the lead for the hosts and keep them in touch of Pep Guardiola's side in the title race.
Klopp made both substitutions when the game was goalless and they proved to be a masterstroke by Klopp.
Only Steven Gerrard has scored more goals against Everon than Origi and Klopp was full of praise for his striker who has been linked with a move away from Anfield this summer.
"We will never miss a player like him because if he leaves, he will explode wherever he goes," he told Sky Sports. "He is a world-class striker, he is a legend and will stay a legend forever.
"He doesn't always make the squad which is ridiculous, but he is there when we need him every time. He was involved in both games; everything that we did in the second half, without Divock, wouldn't have happened."
Lampard said he was happy with his team's performance and wanted them to show the same fight in the remaining matches as they look to avoid relegation.
"They're in a different area to us," he told BBC Sport. "They're near the top of the table, they've been together a long time and have a strong style of play.
"We had to be organised and discplined. I couldn't ask for more at half-time except taking our chances. I'm proud and happy with the performance. We have to take that spirit forward to the final games. We'll give everything until the end."