Gibson upset at Wycombe fans
A number of disgruntled supporters vented their displeasure at Sanchez's reign during Saturday's trip to Cheltenham.
They unfurled a banner which read 'Sanchez Out' with the fans dismayed at the decision to sell Sean Devine to Exeter City.
But Gibson has accused the supporters of having short memories and forgetting the sterling job Sanchez has performed during almost four years at Adams Park.
"I feel really disappointed that a handful of supporters chose to behave like that today (Saturday)," Gibson told the club's official website.
"They need a reality check, we are not Man Utd, we are the same as the majority of clubs in our division and the division below. We have to survive.
"Transfer fees are few and far between nowadays, particularly in the Second and Third Division and we have been offered the chance to take some money regarding a player who is going to be out of contract in the summer.
"I think the manager has contributed a fair bit to this club in the last three or four years and I think the supporters should remember that.
"Lawrie gave them the greatest day they are ever going to have and that none of us could have ever dreamed of. That was Liverpool in the semi-final of the FA Cup, let alone Leicester, let alone Wimbledon, and in the last three years we've gone from a team that was down when we came, to mid-table."