Joe Cole was working as a pundit for BT Sport for the Group L clash in Belarus.
Olivier Giroud had gone over six months without a goal in club football – his last was in the 1-0 win over Liverpool in May.
But the Frenchman finally ended his drought with the only goal of the game against BATE.
The goal came at the same ground Giroud scored his 100th goal for Arsenal last season.
He joined Chelsea from the Gunners in January and Cole says he was delighted to see him become a Blue.
“I’m a massive fan,” Cole said on BT Sport.
“I was delighted when we signed him.
“To score 100 goals at any level but to score it for a club like Arsenal and then to come to Chelsea.
“He did great last season, he did great at the World Cup.
“He’s one of them players you like playing with.
“I’m sure Michael would have liked to have played off him.”
Chelsea were not at their best in Belarus but are now closing in on securing top spot in Group L.
And after the game, Giroud admitted his side could have been better.
“The manager kept saying we need to finish first in the group, and the earlier the better so tonight we’ve done the job even if we could have been more efficient,” he said.
“It’s a clean sheet and we won the game.
“We defended very well and they defended cohesively so it was difficult to find solutions at times and stop them on the break.
“I was hoping to score soon because I came back late from the World Cup and I was lacking maybe a bit of efficiency and luck but you always need to keep working hard and keep the faith and that’s what happened tonight.”