David Mooney took his goals tally into double figures for the season when he headed home in the 90th minute to claim the Johnstone's Paint Trophy Southern Section semi-final tie. The east Londoners were forced to play the final 20 minutes with 10 men after midfielder Anthony Griffith was booked twice in four minutes.
Slade said: "I'm really proud of my players. We've dug in and we are still in two cup competitions. As a club, as a fan-base, as a manager and as a chairman we've all got to be really chuffed and happy with that.
"It was a hard game. Yeovil are a very direct side who play with tempo and we had to deal with that side of it and match it. We did that and although it wasn't a great spectacle in the first half we managed to grind them down and we created a lot more in the second period.
"We probably could have had a couple of goals in the second period if the truth be known and I have to say I thought we were denied a stonewall penalty on Kevin Lisbie. But in the end we got what we deserved because I thought we were the best team overall when we were paying with 11 men and also when we went down to 10 men.
"It was a fantastic header from David Mooney, whenever the ball goes in the box now Moons is on the move and he's a threat. He scored a great header at Hull last Saturday and he's done the same again."
Glovers boss Gary Johnson was quick to criticise his side for the defeat in front of their 815 travelling fans.
He said. "I have to say we didn't do very well. Orient have got their goal, the whole game was poor and no-one can be proud of that, neither team. But they've got themselves through and all we can do is to wish them well because they've beaten us.
"But we've now got a lot to do, a lot of soul-searching to do because unfortunately we had a few players that didn't turn up. I don't think they meant not to turn up but we certainly didn't play near to how we've been playing in the last couple of weeks.
"It was a scrappy game and we weren't able to rise above it. I'm really gutted as a manager because I don't like losing games, any games, and certainly not scrappy games. You have to do a bit more than we did to earn a result."