Sandro did not make the matchday squad for the London derby and tweeted on the morning of the match to clarify that he was not injured, posting: "Good morning guys, just to let you know that I'm not injured! Hope that we can win the game today."
The tweet was seen as a swipe at his manager, but under-pressure Sherwood insisted he had no problem with the Brazilian.
"I don't care about the tweet," the Spurs head coach said after the 3-1 victory over Felix Magath's strugglers. "I don't go on Twitter. He can tweet what he wants.
"I like Sandro's qualities, but in my eyes it wasn't right to put him in the squad - other people are ahead of him.
"I think Nacer Chadli's done well in there and I think Paulinho's done well in there.
"At the end of the day you always get an honest opinion from me and he's right what he's tweeting - he's not telling any lies.
"He's not injured, and he's fit to play, but he's not selected because he's not up to it at the moment ahead of other people."
Sherwood stressed the 25-year-old remained in his plans, and could work his way back into the squad before the end of the season.
Speaking about upcoming matches against West Ham and Stoke, Sherwood said: "We might look for some different qualities in there.
"But for today's game he's not in the squad and he's not selected.
"I really don't have a problem with him. He's a good lad. I don't have any problem with anything he's got to say. He's not being disrespectful to me, I don't think."
Sherwood was also left playing down a heated discussion between Spurs coach Tony Parks and defender Danny Rose towards the end of the match.
Asked about the incident afterwards, Sherwood said: "It was an altercation regarding who was marking who. I think they made a substitution and Danny was a little bit unclear on who he had to mark because the player he was assigned to had already gone off.
"It was a little miscommunication. Tony told him, he was told, and that was it.
"I'm all for that, because it shows they both care and they both want the same. They're shaking hands in there and there's not a problem with that."
Spurs looked on course for a routine victory when Paulinho converted Christian Eriksen's cross before the break, but were pegged back immediately by Steve Sidwell's composed finish.
Harry Kane restored Tottenham's lead early in the second half before another Eriksen set-piece presented captain Younes Kaboul with an easy finish for the third.
There was a late scare when Fulham earned a penalty from an Eriksen handball, but Hugo Lloris beat away Sidwell's spot-kick.
The triumph kept alive Spurs' hopes of European football next season, but was unlikely to dampen any rumours regarding Sherwood's position as manager.
When asked about his future, he said: "It's been five and a half months since I've been in the job and it's never gone away. I'm always fending off the same questions.
"It's not ideal, but it's an environment that's been created and it's a great honour to manage this football club. I just have to be professional and try and prepare them to win football matches as best as I possibly can."