Kubel, who was signed to a two-year contract during the offseason and replaced Parra in the starting lineup, was 0-for-6 in the first two games of the season.
Gibson was asked after Saturday's game if he thought Kubel was pressing.
"Could be," Gibson said. "It's hard to tell. I asked him about that and I told him to relax and play his game. He'll be fine. He'll be fine."
One of the biggest challenges for Gibson this year figures to be how to get Parra enough at-bats to keep him happy and productive. Parra had his finest professional season in 2011, hitting .292 and winning a National League Gold Glove Award.
Gibson is also trying to give each of his position players a start early in the season. Sunday also marked first baseman Lyle Overbay's first start, while backup shortstop John McDonald started Saturday.
That leaves infielder Geoff Blum and catcher Henry Blanco as the only two position players not to get a start.
"When we get to San Diego, I'll try to get the other guys in at some point," Gibson said, referring to the team's upcoming road trip that starts against the Padres on Tuesday.