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Shaw played the full 90 minutes on Tuesday evening as England secured top spot in Group D and a place in the last-16.
Mourinho managed Shaw at Manchester United for two and a half seasons and the pair had a frosty relationship.
Despite being impressed with the Three Lions performance as a whole, Mourinho wasn't thrilled with their quality from set-pieces.
He told talkSPORT per TEAMtalk: "The negative thing I would say is once more they were very poor on attacking corners.
"The service was dramatically bad. They have so many good players to attack corners. The crosses are not passing the first man.
"Luke Shaw, in my opinion, very good tonight but very poor on the corner. [Kalvin] Phillips, the same.
"England has great power at this level and going to knockouts, one corner can decide a game."
Mourinho thinks England are in a strong position, with players such as Harry Maguire and Jordan Henderson to return to full fitness.
"I keep saying when you have an option to take 26 players, you have to risk, gamble and take an injured player if the player deserves that. Maguire is one of those players," Mourinho continued.
"He was confident, he was stable, he was intelligent, read the game well, and has a good partnership with [John] Stones.
"[Tyrone] Mings is doing a fantastic job, you could feel he was happy to come in for 10 or 15 minutes, he is a team player.
"I wouldn't be surprised if the next game is against Germany, the way they play with three at the back - I wouldn't be surprised if England went with Stones, Maguire and Mings at the back."
Gareth Southgate's side have qualified without conceding a single goal in three games, but some fans are concerned by the lack of attacking threat.
Mourinho has countered that by complimenting the 'very good' mentality in their camp.
"It looks good, the players are in good form, [Jadon] Sancho was ready for every second he was on the pitch. The mentality inside is very good," the 58-year-old continued.
"Today they showed two different versions. Great mobility in attack and great creativity. Second half they were a team of position, great positional play and control, you need that in the knockout stage.
"People are not over the moon because people are always asking for more and different kind of football, but inside the camp - they will be happy. They will feel they did the job well and they're ready.
"The next one is the one because it will be against a top team. Yes, an advantage because of Wembley, but pressure because it will be a big opponent.
"If they go to the quarter-finals, this match could be the one which pushes them all the way."
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