The 27-year old Welsh midfielder signed with the Eagles on deadline day for an undisclosed fee, believed to be around £750,000,and his fellow countryman Matthews suggests it was a move that really favoured his former Cardiff City mate.
"It's sad to see him go but I think it was best for Celtic and Joe," he told the Daily Record.
"Celtic have made a bit of money and Joe has a chance to play in the Premiership. Although I'm sad to see him go and he was a big player for us, I hope he does well.
"It's personal preference really. He wanted to play in the Premiership and he got the chance. I think he would like to have stayed but circumstances made him have to leave.
"He leaves a better player than the one the club signed. Coming up here and playing in the Champions League, you learn in every game. He has got better and I hope he can keep improving and do well in the Premiership.
"He will be missed on and off the pitch."
Ledley made an immediate impact for Palace in his first Premier League appearance on Saturday, scoring the second goal of their 3-1 home win over West Bromwich Albion with a thunderous header from a Tom Ince corner.
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