The late leveller was the Danish striker's sixth goal of the season in all competitions, having only netted three times in 39 outings last term for the Lilywhites.
It extended Preston's unbeaten run to a fifth game and McAvoy said: "Emil has been great and we've just got to keep working with him to make sure he's a strong acquisition for us.
"He's young and learning, so he will make mistakes but I have trust in him.
"He needs to keep believing in himself because he will get opportunities in this team. He missed an earlier chance so the game could have gone the other way for him, but he made sure he stuck the next one away."
McAvoy added that Riis' effort was a deserved reward for his side's display and said: "I thought we deserved the point. They are a team that moves the ball well and, in terms of possession stats, they're top of the division but I thought the best way to compete with them was to go toe-to-toe.
"At times, they broke our press and caused us issues, but we were also a threat every time we went forward.
"They made it 2-1 after I had made a sub, but we did not deserve to lose the game that way, so I made another change to try and get something out of the game and, credit to the boys, they kept going and nicked one right at the death.
"These guys give me everything and, if you do that, you never know what can happen – something can fall to you in the box, as it did."
Home boss Slavisa Jokanovic was left cursing more dropped points in the final throes of a game, having seen his team go down 2-1 to an injury-time Huddersfield winner at Bramall Lane last month.
He said: "We hadn't given them anything during the five minutes of stoppage time but then in the last five seconds, we did not concentrate at a free-kick and it has cost us two points.
"That's the second time we have conceded in those crucial seconds at the end of a game and we've got to be a bit calmer and more relaxed in those situations.
"It was not an especially good ball into the box. It wasn't really delivered with quality, but we have paid an expensive price for our mistake and we need to improve our defending at set-pieces."
On a mixed debut for Sweden international goalkeeper Robin Olsen, who was at fault for Johnson's goal but went on to make a smart save from Riis before his second leveller, Jokanovic pointed out: "We've only worked with him for two days and he needs time to adapt to us, as we need time to adapt to him."