Liam Delap's opener was canceled out by Fulham's Adama Traore before halftime.
Woolfenden later said: “The boys stuck at it the whole way through the game, worked really hard and are probably feeling disappointed that we didn’t come away with three (points),” said the 25-year-old.
“At the same time, it was a good performance out there, a lot of new faces out there, a lot of encouraging signs and something to build on.
“To be fair, in the first half we probably weren’t at it 100 per cent, but we still had enough of the ball and (enough to) encourage ourselves that we can get three points on the board.
“Don’t get me wrong, we’re not down in the dumps about it but we felt like we should have come away with three points there. I think (in the) second half, we were massively on top.
“(We) didn’t really create many clear-cut chances with shots but had a lot of good opportunities. We got into the box and it was just that final ball that was lacking at times.
“I think throughout the game we defended very well and (that’s) something as a team we can take great pride in. The way we work for each other when one of us makes a mistake or one of us gives the ball away is unbelievable to see.
“We’re probably a bit disappointed with the way we started the second half against Liverpool after being on top in the first half, so that was something we spoke about a lot after half-time – coming out, raising it again and we did that throughout the whole second half.
“Especially in the last 10 minutes, I think we dominated. On another day, one of the shots falls in, or the final ball is just there, or we’re not quite just offside, and we come away with three points.
“The first two (games) were tough but even then it’s difficult for fans to see that, but we took positives away from those performances. Today, it felt like it really did come into place.”