Moore had initially refused permission for his right-hand man to talk to Swindon boss Danny Wilson but the Tranmere boss was unable to prevent Shirtliff from leaving.
The Rovers boss told the Swindon Advertiser: "Peter Shirtliff's departure was a shock to me. I was away on holiday when I got a phone call from Danny Wilson, asking for permission to speak to Peter.
"The request was refused but there was a clause in Peter's contract that enabled him to speak to Swindon - which he did.
"If someone offers more money to go elsewhere, then there's not a great deal we can do.
"Maybe deep down he thinks Swindon are going to do better than us next season - so that's a challenge for us."