Sharp lost Louie Jacob on Saturday but struck the opening goal in Doncaster's 3-1 defeat to Middlesbrough on Tuesday before unveiling a T-shirt bearing the words 'that's for you son'.
Fans and players at the Keepmoat Stadium gave a minute's applause to celebrate Louie Jacob's short life and Derby continued the tributes on Wednesday during their Championship match against Cardiff.
Tribute: Jason Shackell (centre) was one Derby player wearing a black armband
Nigel Clough's side did not enjoy a happy night on the pitch, beaten 3-0 by the Bluebirds, but Sharp praised the Rams for their gesture.
He said on Twitter: 'Just like to thank derby county football club if its true that the team wore black arm bands as a mark of respect. #touching'
Sharp has opened his heart on dealing with his sadness. In a series of posts on Twitter on Wednesday he wrote: 'To captain the side tonite was an honour and a pleasure, the minute applause I was crying meant so much to me thanks to both sets of fans.
'My goal tonight was the most important goal of my career dedicated to my brave boy luey jacob sharp I love u son sleep tight. thatsforyouson.
That's for you son: Billy Sharp dedicated his goal on Tuesday to Louie Jacob
Minute's applause: Doncaster paid tribute to Louie Jacob before their game
'My goal had to be something special tonight for my special boy. I'm so proud of him, and his mum @jadecarlie86.
'Seriously again its took me 2 hours to read all my tweets I'm in total shock for all ur support u have shown,love to you all.
'I am absolutely overwhelmed with the support from ppl all over the world has given to me tonite, I really can't thank u all enough. amazing.'
After the match, Doncaster manager Dean Saunders revealed the trauma Sharp has been through, by saying: 'I know what has been going on all week, the finer detail, and it is worse than you might think.
Anguish: Sharp (left) showed his conflicting emotions when leaving the pitch on Tuesday
'But Billy rang me last night and said he wanted to play because he wanted to score a goal for his son. He hasn't trained, but when he said that, I couldn't refuse.
'He is going to be feeling the pain for a long time yet. But maybe the best thing for him is to come in and train with his mates. This has been hanging over him for a while, but perhaps he can turn over a leaf now and begin to get on with things.
'What is really pleasing is that he banged in a goal for his son, which is all he wanted to do. It was like the story had already been written, and I'm really proud of him. It tells you everything about him.'
Sharp's girlfriend Jade Fair also sent the following tweet: '@billysharp10 & I are grateful for the love and support we have received. Daddy did Luey proud tonight.Sleep tight angel.'
Referee Darren Deadman was praised afterwards for using common sense and not issuing the standard yellow card for Sharp's celebration.
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