The pair made 286 appearances for the Devon club between them, but are now free agents after their deals expired.
"They've both done very well for the club and I would've liked to have kept them," Tisdale told BBC Radio Devon.
"On the other hand, they weren't first through the door in terms of priority and I was honest with them on that."
Tisdale added: "It wasn't a case of me wanting to thin the squad out or move them on, I simply couldn't sign everybody."
Former Wales international Davies, 32, joined Exeter from Northampton in 2012, while ex-Bristol City player Noble, 34, has had two spells with the League Two club.
Tisdale has made four summer signings, taking his squad up to 24 for next season, but there were five players he could not offer deals to.
"They're not necessarily players I wanted to leave, but you just have to make decisions based on using your budget of course, leaving space for one or two young signings and of course the emergence of younger players," he said.
"There was every chance that things would change over the summer - a player leaving or asking if he could be released from his contract, or a player being bought, and then of course the finances change."
Exeter City boss Paul Tisdale says his limited budget meant he could not offer contracts to right-back Arron Davies and midfielder David Noble.