"I am not an advocate of sacking managers," Gartside told Sky Sports News.
"History tells you the longer a manager stays in one position, the more success the club has.
"I think you have got to know the whole situation. I think it is unfair on Sven. He has had a good run as England manager and has got us into a position where we can qualify for the next World Cup and it would be nonsense to change at this stage.
"You can't expect someone to come in and pick up the pieces and run with it. Sven is a good England manager, he has had success and will continue to have that success.
"I think we are positioned in our best place we have ever been to win the World Cup in the next year."
Gartside will hope Eriksson remains, as Bolton chief Sam Allardyce is one of the favourites to replace the Swede.
The Bolton supremo is aware of Allardyce's ambitions, but feels it is too early to talk about a successor to Eriksson.
"Sven has got the job and Sam respects that," added Gartside.
"Sam has been picked by the media and it is not up to the media to pick the next manager."