Shaun Hill has lost the 49ers’ starting quarterback job, coach Mike Singletary said, and Alex Smith will be under center this Sunday against the Colts.

“When I met with Shaun, I told him, ‘You gave us the best chance to win at that time. Done a great job at this point,’” Singletary said at his Monday news conference. “But right now, we need to go with Alex. Alex Smith gives us the best chance to win.”

Smith relieved Hill during the second half of Sunday’s 24-21 loss to the Texans and threw three touchdown passes, all to TE Vernon Davis. Smith, the No. 1 overall pick in the 2005 NFL Draft, hadn’t played in a regular-season game since 2007 and lost the competition for the starting job to Hill at this year’s training camp.

Hill, an eight-year NFL veteran, struggled in the 49ers’ last two games, both losses. He completed 21 of 49 passes for 243 yards and no touchdowns with one interception.