Ex-England star Cole was working as a pundit on the game for BT Sport.
Chelsea went into the match knowing they would qualify for the Europa League knockout stages of the competition with a victory and could even secure top spot if results went their way.
The Blues beat BATE 3-1 in the reverse fixture two weeks ago, with Ruben Loftus-Cheek scoring a hat-trick.
But it was a different scenario in Belarus with the hosts having the better chances in the first half, including Dmitry Baga striking the post with a fine 25-yard effort.
And Cole claimed Chelsea were complacent after the ease of the win back at Stamford Bridge.
“Very sloppy, complacent,” Cole said.
“This here, the lad’s got the ball, you’ve got to spot the danger there if you’re in midfield.
“Barkley’s just a little bit slow there, I think that summed up Chelsea’s (half).
“He’s not out to him tight enough and that could have been Chelsea 1-0 down.
“That would give them something to hold onto if that goes in and they’ll be even more resilient.
“Again here, that’s the zonal marking, he’s got the cross in and they’ve nearly scored.
“Just a sloppy start all round and even on the ball, which is unusual under (Maurizio) Sarri because they’ve been so good.
“It’s just giving them a sniff, giving them something to breathe on.
“That’s what they’re holding on for Bate.
“They think they’ve got a chance now because Chelsea are making them think that.”