The Bhoys suffered a 1-0 defeat to the Italian giants at the San Siro in Milan in the second leg of the Europa League round-of-32 tie on Thursday.
Celtic lost the tie 4-3 on aggregate and saw their dreams of winning the Europa League this season evaporate.
The defending Scottish Premiership giants were on the backfoot after defender Virgil van Dijk was sent off in the 27th minute, but they battled on.
Hargreaves was impressed with the courage shown by the Celtic players, but he was disappointed with the substitutions made by manager Deila.
“They had Commons, who scored 32 goals in 48 games last season,” the former England international told BT Sport.
“He had to come on (earlier than he did). Gary Mackay-Steven was the best player by a mile in the first half.
“I thought they could have easily made a change with Nir Bitton or Stefan Johansen, who didn’t really do anything in the game.
“I thought that the players were brave, but I don’t think that the manager’s substitutions were brave enough in the game.”
The first change for Celtic came five minutes before half time when Gary Mackay-Steven was taken off for Efe Ambrose.
Then just before the hour mark James Forrest came on for John Guidetti. Kris Commons replaced Stuart Armstrong but only in the 78th minute.
Commons almost made an immediate impact when he saw his attempt from 35 yards saved by Inter goalkeeper Juan Pablo Carrizo.
It is easy to criticise a manager’s decisions on hindsight, but perhaps Deila should have brought on Commons earlier than he did.
The 31-year-old attacking midfielder has been in good form in recent weeks and would have added more impetus to the Celtic attack.