Right-back Ethan Ebanks-Landell gave Wolves the perfect start after just five minutes. But they then squandered a hatful of chances and Mattieu Baudry made them pay by equalising on the hour-mark with Orient's first shot on target.
The stalemate saw Wolves slip to third with Brentford leapfrogging them and Orient.
Slade said: "I am very proud of the team.
"Wolves started very well and they could have put the game beyond us in that first period.
"But the important thing was to stay in the game which is what we did.
"In the second period we came into it. We got a goal and we started taking the game to them for 10 or 15 minutes.
"They never give up, they keep going and they have great character and you saw that in abundance.
"A lot of teams would have found it very difficult to go 1-0 down and come back and attempt to take the game to Wolves which is what we did.
"It was a very open game in the last 15 minutes and both teams were trying to win which was really pleasing. It was two genuine sides looking for that winning goal.
"It was a big game and important game for both clubs and we didn't want to lose it."
Orient fell behind when they paid the price for leaving Ebanks-Landell in acres of space on the wing.
Kevin McDonald fed him the perfect pass and Ebanks-Landell let fly with a powerful drive from the edge of the area that whistled past goalkeeper Jake Larkins at his near post.
Wolves should then have turned that advantage into a commanding lead before half-time only for Jake Cassidy to squander two excellent opportunities before Michael Jacobs saw his goalbound shot blocked by Baudry.
James Henry then fired narrowly wide at the start of the second-half and McDonald was denied by Larkins before their failings came back to haunt them.
Moses Odubajo whipped a right-wing centre across the face of the Wolves goal and Baudry had the simple chance of stabbing the ball home at the far post.