Adam Lallana cancelled out Rashford's opener with a late equaliser.
And England international Rashford was disappointed not to win the game.
"We deserved the three points," he told Sky Sports. "I don't think they were good enough to get a draw out of the game or a win but this is football.
"It was a big opportunity missed and we just fell short. Hopefully in midweek we can get a win and it will start a run for us."