The League Two side recovered from a two-goal deficit and almost claimed victory when Andres Gurrieri's last-minute shot crashed against a post.
Sheridan said: "Full credit to the players. They showed terrific spirit and desire to get back into the game and we should have won it in the end.
"I was disappointed to go two down because it wasn't a reflection of the play. Vale scored from a free-kick and a cross and that wasn't very good from us.
"But the lads were brilliant in the second half. There was a lot of pace and purpose to our play and we caused Vale a lot of problems.
"At the start of the season it was obvious we had to look after the ball better in possession and we are doing that now. The improvement in our play is there for all to see.
"The lads were in a difficult position at two goals down, but they kept going and I'm really proud of them.
"We won't get ahead of ourselves because the replay will still be a very hard game, but we will be at home and we've got a chance."
- Sports & Recreation
- Andres Gurrieri