Terry was sacked as England captain this week by Fabio Capello following allegations relating to his private life and Drogba admitted it had been a tough week for everyone.
"It has been a difficult week for us, for Chelsea, for all the club," Drogba told Sky Sports.
"We tried to stay together and focus on the game. It is a matter of time but we will stick together and keep looking forward.
"We offered him (Terry) as much support as we can. The best thing for him is to play. All his team-mates have to do everything for him."
Chelsea coach Carlo Ancelotti paid tribute to Terry after the defender produced a typically inspirational performance.
"John is the perfect captain for Chelsea," said Ancelotti.
"My captain has a fantastic attitude. He is doing very well in every game.
"It is very important for the team to have this leadership. He was always in control of the game. He has a strong mentality.
"He is working for his club and we are happy to have this performance from him in this moment.
"The England captaincy was not my decision and I do not want to judge about this decision. I knew John met Capello but I did not meet with him (John) afterwards."
Ancelotti refused to rule Arsenal out of the title race even though the Gunners are now nine points behind the leaders.
"Arsenal still have a possibility because they are a good team," added the Italian.
"It depends on the performances of Manchester United and Chelsea. I am not sure it will be a race with two horses."
The Chelsea coach was equally delighted with the form of Drogba who has now scored three goals in two games since he returned from the African Nations Cup.
Drogba's brace took his tally to 12 in 12 games against the Gunners.
"We scored an unbelievable second goal," said Ancelotti.
"It was fantastic movement, fantastic passing and a fantastic shot from Didier. This is football.
"Didier did very well and he is in a good moment. He came back from the African Nations Cup with fantastic motivation and continues to have very good performances.
"We defended well and we deserved to win. It was not an easy game as Arsenal did some very good attacking play.
"We wanted to stay top of the league and we did a very good job. I wanted to hug all my players at the end.
"Arsenal had more possession than us but we defended very well in a difficult game."