Rovers announced the capture of defender Jones on a one-month deal from Barnsley on Saturday morning and he was eligible for a spot on the substitutes' bench in the defeat to Crewe.
However, Jones was soon thrust into the action following Danny Holmes' 33rd-minute dismissal in a contest which Rovers eventually lost 2-1 to leave them with one point from their opening three games.
"The gaffer (Ronnie Moore) told me on Friday that with Ian Goodison being injured he might need cover for the bench," Jones explained to Tranmere's official website.
"Anything can happen in football and I ended up getting on after 30 minutes. It's not the ideal circumstances coming on when the player in your position has been sent off but the lads did well with 10 men. We gave it a go and threw everything at them to get an equaliser but unfortunately we came away with nothing."
Even though Jones' arrival at Prenton Park appeared sudden, assistant manager John McMahon explained the club had been chasing the 21-year-old for some time.
"We had Andrai in last season to train with us but Manchester United came calling for him and he went to train for them," added McMahon.
"From there he went to Barnsley so we missed out on him. But he was still on our radar.
"He's a local lad, a good athlete, strong and aggressive, so hopefully he'll fit in to what we're trying to achieve."