Patrik Schick scored twice from the penalty spot, while Malik Tillman and Ibrahim Maza also found the net as Leverkusen made it two wins from two in the league phase. The result extended their winning run to four matches in all competitions.
Martinez was pleased with the way his side controlled the game, praising both his starting players and those who came off the bench.
"We managed the game well, attacked the spaces from left to right and looked for the things we had spoken about beforehand. We started well and finished well," he said.
The coach accepted that Lech Poznan created some opportunities but was delighted with his team's overall performance.
"The chances they had are normal; you have to accept them. This time, the penalties went our way."
Schick was not expected to play such a prominent role, but Martin Terrier's injury forced the Czech striker into action in the 18th minute.
Despite having no time to warm up properly, he scored twice to take his tally to eight goals in his first eight competitive appearances of the season.
Only Patrick Helmes in 2008-09 and Victor Boniface in 2023-24 had previously reached the same milestone for Leverkusen.
Schick credited his physical and mental condition for his outstanding start to the campaign.
"I feel good, physically and mentally, and relaxed. I am training well, and all of that helps me score regularly," he said.
"I want to give everything while I am in this form, and the team can benefit from it too."
The striker was equally pleased with Leverkusen's performance, saying they dominated from the beginning, pressed effectively and created numerous chances.
He also stressed the importance of carrying that confidence into Sunday's Bundesliga meeting with Freiburg.
Martinez praised Schick's professionalism and explained that he had deliberately limited the striker's minutes to keep him fresh for the weekend.
"He is an exemplary professional and is completely committed to the team," the coach said.
"With his talent, we just have to attack well and find the spaces. If the ball reaches the penalty area, Patrik is already there, ready."
Schick wanted to remain on the pitch, but Martínez insisted that managing his workload was important with another demanding match approaching.
The coach's expectations were clear when he summed up the attacking mentality he wants from his players.
"If we score three, I want four. And if we score four, I want five," Martinez said.
However, the victory came at a cost, with Terrier suffering an injury during a sprint before being replaced by Schick.
Martinez expressed concern for the forward, who is highly regarded by his team-mates for both his personality and footballing ability.
"He is an incredible guy, and everyone loves him, not just because of who he is as a person but also because of his football," the coach said.
"He felt something at the back during a sprint. Hopefully, he will be out for the shortest time possible, because he deserves that."
