"I'm quite a realistic person so I know my situation, but I'll never give up - I'll keep pushing," Hamilton told Sky Sports News.
"We've had some strong results, Jenson did a good job today. I think with a bit of a better qualifying we would have had a better result, but the Red Bulls are going to be hard to beat."
When asked about his performance, the 27-year-old responded positively, saying that he got the most out of his car on a tough day.
"Quite happy with my race to be honest," he added. "I was able to look after my tyres quite well, quite long in the first stint.
"It wasn't particularly exciting but I got everything I could out of the car."
Vettel's victory moved him four points behind Alonso in the race for the championship.