North End skipper Mousinho, filling in as an emergency right-back in Saturday's 1-0 FA Cup loss at Millwall, limped off after only nine minutes to add his name to a spiralling Deepdale injury list.
The defeat at The Den came after a trip north to Hartlepool on New Year's Day and Westley's men head to Coventry for the second time in three weeks to contest the Johnstone's Paint Trophy Northern Area semi-final on Thursday night.
"We've had plenty of trips and journeys in the last three or four weeks," Westley told the Lancashire Evening Post.
"When you are sleeping in different beds, and sitting on coaches and trains, you're always going to be a little bit susceptible to strains whatever work you do. We've picked up one or two strains in the last few weeks."
And Westley is unsure over whether he will be able to bring in the desired number of reinforcements in January.
"Losing Mous who was already covering for (Keith) Keane leaves us with more questions than answers," he explained. "It's not as straightforward as just going out and getting someone, we are limited by our squad budget.
"We can't go with the begging bowl to the club and ask to go beyond the budget because there's the rules we have to stick to."