Having fallen to joint-bottom of Super League, the Robins face Salford Red Devils at Magic Weekend in Liverpool on Sunday desperately needing victory.
Dual-code England international Tomkins, 32, has featured at some of the greatest sporting venues.
“Anfield is as iconic a stadium as any in the world; it’s fantastic,” he said.
“People all over the world know about Anfield and it’s a privilege really to come here and play.
“I've played at Old Trafford and Wembley and this is right up there with the great British stadiums.
“It’s probably something that when I retire I’ll look back on with pride.
“But for us this weekend it’s more about getting those two points.
“We could be playing on the local park; we just need to win and can't get too caught up in the theatre of it.
“We really have to get a performance.”
Rovers let yet another slip to lose at Huddersfield Giants last week, something that is becoming a common theme.
They are now 11th, level with bottom-placed London Broncos and Leeds Rhinos in 10th, at the foot of the table on just eight points from 15 games.
The East Yorkshire club did beat Salford less than a fortnight ago to offer encouragement.
But Tomkins - who won a Super League and Challenge Cup double with Wigan Warriors - knows they urgently need consistency.
“It is frustrating,” said the back-row, when asked what it is now like playing for a side that struggles to deliver on a weekly basis.“I don’t mean that in a way where I’m frustrated with the team - we’re all frustrated because we know we haven't given our best account of ourselves this season and it’s probably just subtle things we need to change.
“The main thing is we need to keep hold of the ball and complete our sets. “When we do that we are a pretty dangerous team and dangerous for anybody.
“We’ve shown that this season against Warrington and St Helens - we were the better team for periods of those games and those two teams started the season blowing teams away.
“As soon as we don’t keep hold of the ball and don’t complete at a high rate,we lose a foothold in the game and struggle to stay in it.
“We really have to address that and if we can - and we've done it in patches - we’ll start climbing the ladder.
“But at the minute we’re putting pressure on ourselves and more so the further we slip down the ladder.
“Allied with London getting a win on the weekend that makes us joint-bottom. Although people say ‘we don’t look at the table’ of course you do. “Everyone does. It might even be subconscious but we’re under pressure now and we need to start winning some games.”
Rovers won 32-18 at Salford to reach the Challenge Cup quarter-finals where they host Warrington Wolves next Friday.
Tomkins said: “The second half at Salford was by far our best performance yet. “We completed at 94 percent in the second period, our defence was really on and we were good.
“Salford have got Jackson Hastings and Robert Lui who are one of - if not the - best half-back partnership in Super League on their day.
“We kept them really quiet and when we had the ball we put on some good stuff so we’ve got to try and do that again.”