The ex-Blackpool striker dropped down two divisions to spearhead the Alan Knill revolution at Gigg Lane and made a dream start with the Shakers on Saturday.
Knill chose not to risk Andy Bishop at Chesterfield due to a slight thigh strain, so Morrell was handed his league debut and converted a Mike Jones cross in a convincing 3-1 win.
"Coming to League Two with a big reputation, I wanted to hit the ground running, so it was great to make a good connection and see it go in," said Morrell.
"I understand that there's a bit of pressure on.
"I think I'm way off where I can be but I've repaid the manager a little bit and I hope there's a lot more to come."
Morrell had a full pre-season with Blackpool but didn't play in any of their friendlies as his future was uncertain.
The former Wrexham and Coventry man had offers from League One clubs but opted to join Bury on a two-year deal.
"I got offered a new contract at Blackpool but they wanted me to take a big pay cut and I thought I deserved more respect because I'd done quite well for them," said the Doncaster-born striker.
"They thought at 33 I wasn't able to play that many games so hopefully I can prove a few people wrong with Bury.
"They were one of the last teams to come in for me but it just felt right," added Morrell, who helped the Seasiders to a League One play-off final victory in 2007.
"I did my background on the manager, I know a few players who've played under him and they speak very highly of him.
"The set-up here is going in the right direction, we've got a good little squad, and if we keep everybody injury-free, there's no reason we can't do well this season."
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