The 52-year-old insists his side face strong competition for Premier League survival from club's who have spent heavily
Oscar and Frank Lampard grabbed the goals as Jose Mourinho marked his first competitive fixture since a high-profile return to west London with a comfortable win.
But, even after acknowledging the sizeable challenge facing his team, Bruce was adamant that Hull can survive this season following the match.
"We all know how difficult it's been and what's changed this year for me is that the so-called smaller teams have all invested a lot of money," he said.
"When you see the likes of Southampton going for a £15 million player; Swansea, Norwich, all the teams that - no disrespect to them - you think you're going to be up against, they've all invested too.
"We know how difficult it's going be but let's try to make a fist of it and do our best to try and stay there."
Bruce also explained his decision to omit club-record signing Tom Huddlestone and Tottenham loanee Jake Livermore from his starting line-up.
"We've only had them 48 hours really and believe them or not we've been trying to work on a system to play Chelsea for the last two-three weeks," he added.
"Also I have to say that that in management to create the spirit and atmosphere you have to be kind to the boys who have got you here too.
"For them rainy nights in Barnsley - no disrespect - people have done well for me so it was important for me that they be rewarded too.
"But make no mistake the two boys from Tottenham will make a huge difference to us and we've got many games to play where we won't be playing Chelsea every week."