Speaking ahead of Sunday’s clash with Celtic at Ibrox, McCoist said he hoped for “lots of excitement and goals”.
“I was very lucky as a player against Celtic and hopefully I’ve kept some of that luck,” said the manager of the Scottish Premier League leaders.
“The pressure as assistant manager was very intense and I realise the responsibility is certainly greater.”
Since succeeding Smith in the summer, McCoist has guided Rangers to top of the table, a point ahead of Celtic.
“I understand the enormity of the occasion, having played in so many and being an assistant in so many,” McCoist said.
“I’m not sure it will feel any different because the desire to win and to do well will be absolutely massive.”
I’d be loathe to say who’s the favourite in any Old Firm game
Ally McCoist Rangers manager
McCoist expects a tough game on Sunday and added: “Celtic took more points off Rangers last season and I don’t think there’s an awful lot between the teams.
“I believe we can win it and we’ll be picking a team that can hopefully do that.
“But I’d be loathe to say who’s the favourite in any Old Firm game; especially this early in the season.”
With so many attack-minded players in his squad, McCoist said he would send out a side to win Sunday’s derby.
“You look at Jelavic, Lafferty, Naismith, Davis, Whittaker and Wylde; they’re all boys who are forward-thinking players,” he added.
“It would be wrong of us not to let them go and express themselves.
“There are different ways to win games of football, but it’s safe to say we’ll be sending out an attacking team to go and win the game.”