Republic of Ireland defender Sean St Ledger fired home from close range in the fifth minute of stoppage time to break the League Two club's hearts.
Jo Kuffour's superb strike drew Wanderers level before half-time after David Nugent's penalty had put the Foxes in front.
Pearson could not hide his delight at how his side had got the job done without the added stress of extra time.
"Competitions are always going to throw up difficult games and we were expected to win this, they had nothing to lose and I thought it was a good game of football," said Pearson, whose side host Leeds in their first home game of the Championship campaign on Sunday.
"Both sides wanted to win it and we got that late goal, we had plenty of chances and they have scored a strike that is of exceptional quality.
"These games are never easy to negotiate and I'm glad to get through it in 90 minutes, sometimes it does not go your way but it went our way.
"I thought our delivery from set-pieces was very good and we were able to sustain the pressure towards the end and get the goal that we needed.
"We did not do what we talked about before we went out, looking at the footage and reports we have got of them, we knew they were disciplined and work very hard and they have some very good players as well."
- Sports & Recreation
- Sean St Ledger
- David Nugent