Lallana went into the game amid the club's row with ref Mark Clattenburg.
Rodriguez said: "He has gone up a level since England.
"The England trip was really good for us, belief and confidence- wise.
"To go and play with the players in the England squad was massive for us. He was brilliant when he came on. He always is when he plays. He is the playmaker.
"He has come on and scored and been influential in his play, so he is a pleasure to play with."
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