Parlour thought that Chelsea were starting their games at a slower intensity and tempo but it was a different story when they came up against Paul Lambert's men, with Oscar giving the home side the lead inside seven minutes.
He told Sky Sports' Morning View programme: "What they did better was how they started the game. I went to the Swansea game and the Leicester game, and they started really slowly - after 25 minutes the away team was the better side. But this time around, I think Jose Mourinho will have been working on that and with the players, saying 'we have to start quicker, we have to better at the start of the game'."
Chelsea currently sit top of the Premier League and Diego Costa has played a large part in that after signing from Atletico Madrid this summer. Despite struggling with hamstring injuries, Costa has found the net on eight occasions for his new club in the Premier League, and Parlour said it wouldn't be surprising if manager Jose Mourinho wants to wrap him in cotton wool.
Parlour added: "If he's playing like that week in, week out, scoring goals you're going to wrap him in cotton wool. That's probably the only concern Jose Mourinho has got.
"They will create lots of chances with the midfield they've got and now, which they haven't had over the last couple of seasons, they've got someone who can finish."
Whether Costa's fitness has improved significantly or not will be shown this week when the side heads to Lisbon to take on Sporting in the Champions League. Costa has sat out the midweek matches so far this season to nurse his hamstring problem.
Mourinho has said he needs time to get him fit for two games per week, though with him reportedly having to sit out training sessions, it would be a surprise if he were to start in Portugal.