The Mexican was left without a seat after McLaren decided to replace him with Formula Renault 3.5 champion Kevin Magnussen near the end of the season.
With Perez not willing to drive for one of the back-of-the-grid teams, the 11th-hour Force India deal meant he will remain in grand prix racing for another year.
"I was close [to leaving F1] because the [McLaren] decision came very late, and I was not willing to join the smaller teams," Perez told AUTOSPORT.
"I am very hungry and willing to prove myself in F1. I always thought if I don't get the Force India drive it would be difficult to stay in F1. Luckily we got that, now we look forward to the future."
Perez, who will partner Nico Hulkenberg at Force India next year, has the clear goal of proving he can shine in a top team after a difficult season with McLaren.
"Of course, to prove myself to the top teams once again," he said about his goals for 2014.
"I did it last year, so I don't see any reason why I cannot do it again. I have confidence in my talent and I know what I can do."
Although the Mexican conceded it was hard to be left without a seat at McLaren, he hopes the move will eventually be for the best.
"We never know what the future holds, especially in Formula 1, so what I am hoping to is look back in a few years time and say this was the best thing that could have happened for my career," he added.
"Hopefully joining Force India will be really good for my career in F1. Obviously I have big targets and dreams, and I want to make them happen."