Many feel that the display of the youngster would earn him a starting-spot when England open their World Cup campaign against Tunisia on June 18.
However, when asked if Rashford deserve to start, Big Sam told talkSPORT: "Er, probably not, no."
"If Gareth is thinking about rotation, using the full strength and depth of his squad, I think he [Rashord] will come in in the group stages and start a game," Allardyce added.
"Looking at all the changes Gareth made to the team yesterday, and I know it wasn't big opposition but given how well they performed, I don't think he'll pick the same XI for all three group games.
"I think he'll use a rotation system, which is very important if you're going to go a long way in the World Cup."