The midfielder, borrowed from Sheffield Wednesday, celebrated by jumping into the Blackpool fans and took his shirt off, which earned him a booking.
Parkes said: "We've lost three wide players and we needed a player who can give us width and we remembered Wade.
"We went to Sheffield Wednesday and Brian Laws agreed to us taking him on loan. He was very excited when he scored and the players said they thought they had lost him when he jumped into the crowd.
"I thought he wasn't going to come out of the crowd. It was a really good reaction from him."
Parkes added: "We needed that kind of finish. It looked like we weren't going to score.
"It had 0-0 written on it. We have had three good results in a week and we've taken seven points out of nine.
"It's important that you take points off teams around you. We have done the double over Barnsley."
In the first half, Small missed an easier chance in the 11th minute when a Martin cross from the right found him unmarked and he shot wide from six yards.
Barnsley boss Simon Davey said: "It wasn't the result I was looking for.
"We didn't step up to the plate. We are disappointed but we've got 11 games left and when it comes to May 4 then we'll decide how well we've done.
"It's not going to be judged on one day. It was a big game for us and we lost it and that's what happens in this division.
"Nothing dropped for us and if we were still out there now, we wouldn't score. It's disappointing because we lost at home and lost to a team that's around us."
Barnsley thought they should have had a penalty three minutes before the interval when Michael Mifsud went down in the area but the referee waived away the appeals.
Davey said: "I thought it was a penalty but the referee didn't and he didn't have a bad game."
Barnsley's on-loan signing Adam Hammill had a good game against his former club.
His best chance came two minutes before the break when his shot from the edge of the area which deflected over Blackpool keeper Paul Rachubka but went just over.
In injury time Hammill curled his free-kick around the wall and Rachubka had to tip it round the post.
Davey added: "Adam looked dangerous all game and the keeper pulled off some good saves."