The Nerazzurri found themselves down 2-0 at half-time, but goals from Diego Forlan and Diego Milito in the last 20 minutes allowed them to scrape a point.
Sunday's draw extends Inter's winless streak to nine matches in all competitions, amidst speculation that former Chelsea coach Andre Villas-Boas could take over at the club.
"My position? The important thing is Inter, I try to do the best for the team," Ranieri told Sky Sport Italia after the match.
"I have a two-year contract and I hope to stay. I think about working and doing the best I can.
"This is not a simple case, but I believe."
The 60-year-old then admitted that he is in the dark about what president Massimo Moratti is thinking.
"Every time we have suffered a defeat, he supported me, but he cannot do anything else," Ranieri asserted.
"This is like a marriage, the husband is always the last person to know what the wife is doing."
Ranieri then hailed Inter's never-say-die attitude against Catania, but rued that his side continue to concede goals too easily.
"At the first opportunity, our opponents scored a goal, and the moment we get a scare, we lack determination," the 60-year-old continued.
"We got off to a good start, but then we became quiet with their goal.
"I have great champions who looked each other in the eyes and they came out with a great reaction."
The Italian coach also commented on playmaker Wesley Sneijder, who was introduced in the second half and turned in a good display.
"He is a champion, so it is normal that I always have to talk about him, but we have to give him time," Ranieri explained.
"He is finding himself and he will help us in the future."
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