The captain was dismissed for another relatively low total in the evening session on day four at Lord's, leaving him with a top score of 28 from his last seven innings.
The assistant coach told BBC Sport: "Alastair is our leader, our captain and he's got the full backing of our dressing room.
"You saw how the people in the ground genuinely wanted him to get runs. People are behind him. We want him to carry on as our captain, he's a good man, a good captain and he's getting better with every game."
England will resume on 105-4 tomorrow, chasing 319 for victory.