The 20-year-old took his tally to five goals in the space of five days after his double in a 2-0 win at West Ham United on Monday.
Wilson completed his treble during the opening 45 minutes, and Critchley was keen to single out his all-round contribution to the cause.
“Harry was a real attacking threat for us and it was great to see him get his hat-trick,” Critchley told Liverpoolfc.com.
"The first goal he scored, his header, he made it look easy when it was a difficult header.
“We said to him at half-time that even though he got his hat-trick it was important not to think his job was done and I thought he did a really good job for the team, especially his defensive play. That is an area of his game he has improved on from last season.”
The victory over Spurs saw the U23s extended their record to six straight victories in Premier League 2.
While expressing his delight at getting another victory, Critchley still felt there was much for his team to improve on.
“It was a little bit indifferent because I didn’t think we were at our best,” he added.
“Obviously we scored some cracking goals and we had some lovely moments and some really good passages of play, but I just felt we were a bit sloppy in our play.
“We started like a house on fire, but maybe going 2-0 up so early on was the worst thing that could have happened to us because we took our foot off the pedal and Tottenham punished us for that, but we showed good character to respond to that.
"[As a coach] I just never felt comfortable all the way through the game. It was our second game in five days and you could see the lads were a bit tired towards the end of the game but we saw it our well.
“We are always looking for improvement. The next step hopefully for these players is the Premier League for Liverpool, so we want to replicate the first team as much as we can.
“To get an opportunity to play at Anfield in this unbelievable arena under the lights on a Friday night doesn’t get much better.”