Dylan Mottley-Henry's first-half goal sealed the tie for the north east outfit.
"It's extremely disappointing. We're gutted to get knocked out of the FA Cup. It's a massive competition which we wanted to do well, but I must say we didn't turn up on the day," said Daws.
"We were second best and for the first time since I've been taking the team, we didn't really look like scoring, although we had a couple of half-chances in the first half at 1-0 down where we perhaps could have equalised.
"We tried to prepare the players correctly and professionally like we always do. It was a game we wanted to do well in and an opportunity to progress in the FA Cup but we just weren't at the races. We were too slow in possession of the ball, we didn't pass it quickly enough to try and shift the opposition, and going a goal down so early didn't help. It was disappointing coming from a set-play. A couple lads switched off and we got done.
"After then, South Shields used that as a chance to sit back and soak it up with two banks of defenders and midfield players, with Dylan Mottley-Henry up front and tried to hit us on the counter-attack with the long ball over the top to use his pace.
"We didn't have enough quality over the halfway line with our final pass, shot or whatever it was to open them up."
See more from Tony Daws and Andrew Boyce on Iron Player.
