Striker Hanson was forced off after just 18 minutes in Saturday's home win over Wycombe and midfielder Syers was withdrawn midway through the second half. The two players have scored 15 goals between them this season.
Taylor said: "It's the story of our season at the moment, we haven't been fortunate with injuries.
"James has picked up a groin injury and David has a hamstring injury, so they both look like they're going to be out for around two or three weeks.
"It's a really frustrating situation, but thankfully the players that did come in after the injuries performed well."
Skipper Simon Ramsden (hip/calf) and fellow defender Lewis Hunt (knee) both returned to the starting line-up against Taylor's former club following long-injury.