The hamstring injury which has led to Cole's absence for around two weeks is set to give the 23-year-old a run of games to prove himself as a genuine rival to his senior team-mate.
"Personally it's a chance now for me to come and play in the next few games," Bertrand said. "It's just down to me to keep training well, keep my performances up to a level and keep pushing and pushing and pushing until the time comes."
He added: "It's just important I focus on the next game and make sure we get the right results. For me it's about getting in game time and trying to put in as good performances as I can."
Bertrand has won the Champions League and FA Cup and twice played for England, but has missed out on selection since winning his second cap against Ukraine last September.
"It's just about focusing on my club game and I'm sure if I get enough games and my performances are hopefully good enough that should take care of itself," he added.
Bertrand has made 32 appearances for the Blues this season and played down the torrid time he experienced against Shakhtar Donetsk in the Champions League last November.
"I just think that was another game and valuable experience and learning curve for what may come in the future," he said.
Chelsea interim boss Rafael Benitez was asked about Bertrand's improvement as the Blues, last season's Champions League winners, seek to succeed Atletico as Europa League winners. Benitez said Bertrand had progressed during his tenure, along with Victor Moses, Cesar Azpilicueta, David Luiz, Oscar and Juan Mata.
On his most-improved list was also Frank Lampard, who appears to be in the final months of his Chelsea career, and Benitez said: "He (Lampard) has been doing really well for us. When I came (in November) he was injured. He was scoring goals at the beginning, he was scoring more goals after that. He has improved - his form, at least, during this season."
Source: PA
Source: PA