The Barca boss made eight changes to his starting XI from the Copa del Rey win over Villarreal in midweek with Lionel Messi's hat-trick and further goals from Neymar and Luis Suarez helping the Catalans move within a point of leaders Real Madrid.
And Bartra, who set up Messi's second, is hopeful of contributing more towards Luis Enrique's bid for trophies.
"This big win is a result of the hard work we do in training. We are feeling fit and are all playing a part in this good run," he told reporters after Barca's 11th consecutive victory in all competitions.
"The most important thing is that we maintain the same level when us less regular players get a game. Or to even improve the level if we can.
"If the boss needs me, then I'm always ready to answer his call. I need to be ready to help out at any time."
While Levante initially frustrated their hosts, Messi's quality eventually paid off as the Argentina captain marked his 300th Liga appearance with a hat-trick - with Bartra providing the assist for his first goal before half-time.
"When teams come to the Camp Nou we need to suffocate them, put pressure on them and not let them out of their half," Bartra added.
"I set up Messi’s goal today, but he did the most difficult bit."
