The former England international scored a second-half winner against one of his former clubs to secure The Hoops' first away win of the season.
"If Chelsea struggled to break us down, with the way we played against them, then a lot of teams will," he told reporters.
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"We've never stopped believing we could escape ever since we got in this situation. We still believe it strongly and it was a great relief to get that result at Stamford Bridge.
"Away from home we haven't been the best and we've dropped a lot of points, so this is something we have to consolidate now.
"We tried to frustrate Chelsea and catch them on the break and we did that well."
Jamie Mackie also feels he and his team-mates must use this win to launch their survival bid and feels surprise points are vital in remaining in the Premier League.
"It's important that we continue displaying the belief we showed last night, otherwise a massive result like that can be wasted," Mackie told talkSPORT.
"When we stayed up last season we got an unbelievable result against Liverpool when no one expected it. It gave us belief, we got some results and it kept us up.
"We weren't good enough when we lost 3-0 to Liverpool and it hurt as a professional.
"At Chelsea, we worked for each other, there was no selfishness out there and that is the only way to get out of trouble."