Woodward came in for criticism after Pedro moved to Chelsea, rather than United.
But the United boss maintains he has a good relationship with Woodward and has faith in his ability to bring the best players to Old Trafford.
"I have the idea you want to separate Ed Woodward with me
Never
Never," the United boss said in a spiky press conference.
"Because every day I am updated by him and I trust him."
Van Gaal added: "I don't think they (the critics) have to doubt Ed Woodward because he has proven already for many, many years he is the right person on the right spot."
United were aware for some time that Pedro wanted to leave Barcelona after becoming frustrated by a lack of first-team football.
It was reported that Woodward flew into Barcelona on Monday in an attempt to finalise a deal for the 28-year-old, who had a buy-out clause of 30 million euros (£21.5million) written into his contract.
But three days later, the World Cup winner signed for Chelsea.
At a press conference last week, Van Gaal said Pedro fitted the profile of the kind of quick and creative player he wanted.
But when asked about the forward this week, the Dutchman refused to divulge the reason why he had not signed the Canary Islander.
"I cannot answer these questions," Van Gaal said before launching a tirade at the media.
"When you ask me, 'Is Pedro fitting the profile?', I cannot lie, I said 'Yes'
But I do not say that I'm interested in the player
That is the difference
But you say I'm interested
No, I answered the question
It's different.
"What is written in the newspapers is not true, you cannot know it
Only the players know it and the clubs know it."
Source : PA
Source: PA