Mowbray wants his remaining players, as well as those he brings in during the transfer window, to take on more responsibility as a result.
And despite only recently turning 22, Spanish midfielder Crosas is happy to do just that, urging his team-mates to follow suit.
"We are young guys but we've been playing a lot of games, not only for Celtic but for other teams also," he said.
"Yes, we need to take that responsibility and I think maybe I have to step out and take a bit more responsibility than I had before."
Former Barcelona youngster Crosas does not believe he needs to alter his relaxed approach to the game in order to achieve this.
"Every man is how he is and not because other players leave," he said.
"I'll maybe take more responsibility on the pitch but I'm not going to change how I am."
Crosas will look to help Celtic avoid an Active Nation Scottish Cup upset when they travel to Morton for their rearranged fourth-round tie tomorrow night.
The Hoops go into the game on the back of damaging draws against Rangers and Falkirk in the Clydesdale Bank Premier League.
Saturday's result against the Bairns prompted defender Andreas Hinkel to question the number of "strange decisions" that have gone against the Parkhead club in recent weeks.
Crosas insisted referees were not to blame for Celtic's recent results but added: "I think Andy didn't say anything wrong.
"He just said for the last few weeks, we had strange decisions against us. He was right."
Slipping nine points behind Rangers has put extra pressure on Celtic to avoid a cup upset at Cappielow.
"It's important because we're not doing as well as we'd want to be in the league," Crosas said.
"We need to do well in the cup."
The Spaniard is adamant the SPL can yet be won, saying: "We're still in the league also.
"We still have our chances.
"We want to win this cup and win the league also."
Crosas knows Morton will come out all guns blazing in a bid to further derail Celtic's season.
"Everyone wants to play against Celtic or beat Celtic," he said.
"We need to be ready for that."
The midfielder is also braced for a difficult pitch, which has not been fit to play on for more than a month.
"I know they called off the game two times and it's not going to be the best," he said.
"But, as a footballer, you need to be ready for that also."