Trailing at half-time to City, who had been reduced to 10 players when Georgia Stanway was sent off late in the first period, United came out after the break looking a much-improved side and found two goals in quick succession in the 72nd and 75th minutes.
City responded equally well, Ellen White tapping home from close range to bring the scores back level, but despite his team being unable to find victory and three points, Skinner was pleased with his players.
"A little bit mixed," was his summary of his thoughts after the game to MUTV.
"We wrestled ourselves into the lead in really good psyche.