The assistant coach at the four-times European kings believes the exertions of the 2011 World Cup and the recent RBS 6 Nations have had a negative impact on a Toulouse squad packed with international stars.
"We were poor against Edinburgh and I know what caused it," said Elissalde.
"Individually and collectively the players did not have a good Heineken Cup tournament. Some of the players played a lot during the beginning of the season in the World Cup and then played the Six Nations and so they had a short amount of time in which to recover. After that, it's hard to avoid the underachievement and the doubt.
"If we underachieve again this weekend we know where the struggle comes from. It's due to a lack of players, a tired squad and a lot of injuries in the same positions."
Toulouse were beaten at home by Harlequins and then at Gloucester in the pool stages of the Heineken Cup, the first time they had been beaten twice in their group since the 2007/08 season.
But despite missing out on a home quarter-final as a result of those two losses, Toulouse travelled to Edinburgh as heavy favourites given the Scottish side's lack of experience in the last eight.
Edinburgh upped their game at Murrayfield, though, leaving Toulouse to turn their attentions to the defence of their Top 14 crown - a defence that continues with a trip to Perpignan this evening.
"We had a bad weekend and we have been eliminated from the Heineken Cup," added Elissalde.
"We would have liked to have produced a better performance but our job now is to remobilize the squad. We have already qualified for the Top14 play-offs and we have the opportunity to keep our title. We need a reaction and a fresh start.
"The players have discussed their performance against Edinburgh between themselves and also with us the coaches. We are there to help them not to beat a "wounded beast".
"There are always some doubts after a defeat but we have to deal with it. I am sure the team is mature enough to start again and finish the season well.
"Personally, I didn't wait to loose a game to take a new look at myself as a coach - I am always learning. It is true, though, that it was my first big defeat as a coach and loosing a game because you played very badly is a headache I haven't yet known."