Leah Galton opened the scoring for the Reds in the first half, but her goal was cancelled out by Laura Coombs' equaliser after half-time.
Following the draw, which could have gone either way, Le Tissier told club media that Skinner's side wanted more than just a point from the derby.
"[We're] gutted," she said. "It's just one of those games where we think we've done enough to win the game but of course they're a great side.
"Credit to them, they made it hard for us, but we're gutted.
"It just shows how far the team's come that we're gutted with a 1-1 draw to City, but it's a game that we wanted to win.