The former Liverpool and Blackpool striker came off the bench for his first Jags appearance on Friday night during the Scottish Premiership clash with Saints.
But his night was spoiled when Kenny McLean netted a penalty winner deep into injury-time.
Thistle have a swift opportunity to gain revenge when they host the Paisley side in the third round of the League Cup on Tuesday night.
“That’s the good thing about football, you always get the next game to put it right,” the 23-year-old said.
“It’s a bit unfortunate to concede a goal so late in any game but we hopefully we can put it right on Tuesday night.”
Eccleston had watched his new team knock Inverness off the top of the Scottish Premiership the previous weekend and he has got good vibes about the club despite the initial disappointment of his debut.
“I have been here a couple of weeks and picked up a bit of a thigh strain during the international break so it was good to get on the park,” he said. “But obviously it was disappointing to get the loss.
“I watched the game the previous Saturday and was very impressed with the standard. Since I’ve been here the atmosphere around the training ground has been good.
“We have had some really good training sessions and I think we have some very good footballers in and amongst the squad, so I’m very excited.”