Rovers trailed 1-0 at half-time at Stamford Bridge due to Gael Givet's own goal and were indebted to goalkeeper Paul Robinson for still being in the contest.
However, Chelsea fired in four goals in the space of 16 minutes after the break to leave Blackburn boss Allardyce fuming at his players.
"The second half was pathetic," declared Allardyce.
"I didn't see that coming. I felt we had set our stall out to frustrate Chelsea as best we could and it worked very well in the first half.
"We knew it would have been difficult to get something out of the game, but why throw a game plan that is working so well out of the window? That is what I cannot understand.
"At the moment they are not good enough. Bottom line. Mentally resilient? Not there. Physically challenge the opposition? Not there.
"If you play football away from home in the Premier League, it doesn't get you results.
"You need all the elements to go with it and we have not got them away from home.
Bitterly disappointed"We have not got resilience, the mental toughness and physical presence we should have to play away from home and win a game of football.
"Our defending side was looking very solid and very good and we were limiting Chelsea to shooting from outside the box.
"But we went pathetically wrong. All the tactics we had set out went out the window when the second goal went in.
"We felt we had to go and attack even more and when you are playing against a side of this quality, they just go and score more goals.
"So I am bitterly disappointed with the players and their lack of understanding of the situation they put themselves in.
"Instead of making themselves more difficult to beat, they made themselves easier to beat after the second goal and that's why we got beat 5-0.
"Great players Chelsea, they take advantage of everything you give them and took advantage of our naivety with some great goals."