The Lakers missed the playoffs for the sixth successive season after finishing 2018-19 with a 37-45 record, despite the arrival of superstar LeBron James.
Los Angeles parted with head coach Luke Walton, while Magic Johnson stood down as president of the Lakers.
However, Pelinka is confident about the Lakers' future, especially after the franchise received the fourth pick in the upcoming NBA Draft.
"I think if people take a look at where this franchise is right now," Pelinka told reporters on Monday. "We have a high draft pick. We have a great young core, maybe one of the best in the league.
"We have a superstar on our team, and an open slot. So, I think people can look at this as an opportunity to win a championship possibly next year."
The Lakers entered the season with high expectations after James left the Cavaliers and signed a four-year, $153.3million contract.
Los Angeles opened with a 20-14 record before James strained his groin on Christmas Day. He missed the next 17 games and the team never recovered.
Los Angeles also dealt with injuries to key role players — including Brandon Ingram, Lonzo Ball and Kyle Kuzma — throughout 2018-19.
"We know the characteristics and qualities we stand for," Pelinka said. "And we know as a staff and feel very strongly that if people judge and evaluate us for who we are as an organisation and the vision and path we have going forward, we feel there will be a very, very strong appeal for the great players to come here."
Magic Johnson, who shockingly stepped down from his position as the Lakers president of basketball operations before the team's final game of the season, blasted Pelinka and accused him of "backstabbing" during an interview with ESPN earlier on Monday.
Pelinka denied Johnson's accusations at the news conference — which was held to introduce new Lakers coach Frank Vogel.