Finn's place in the team is in jeopardy after he toiled in the second innings of the 14-run victory that saw England seize a 1-0 lead in the Ashes series, and he could make way for Tim Bresnan or Graham Onions.
The 24-year-old was targeted by Australia on the final day at Trent Bridge, resulting in his withdrawal from the attack after only two overs.
Former England seamer Gough, however, insists he suffered because of a pitch that offered him little.
"Without a doubt he should continue in the team. Before the series starts you pick your three best seamers and they're Jimmy Anderson, Stuart Broad and Steve Finn," Gough said.
"Just because he had a poor second innings does that mean we drop him and we go with someone else?
"He had 20 overs of bowling in the first innings and was on a hat-trick having got the breakthrough by getting two important wickets.
"In the second innings he didn't come on until the 36th or 37th over and if you're a fast bowler on that pitch, if you don't bowl with the new ball you're open to being attacked.
"The Aussies went after him because it was a slow pitch and he's the quickest of our bowlers, making him easy to score against.
"If a batsman had one poor game you wouldn't be saying let's leave him out, he'd get more of an opportunity. It should be the same for bowlers. Finn deserves more than one game, especially when the previous pitch didn't suit his bowling."
Lord's is home to Finn's county Middlesex and Gough, who played 58 Tests from 1994 to 2003, believes he will benefit from the familiarity offered by the ground.
"When you get to Lord's it might be slightly different because he's used to playing there, we'll have to see what the conditions are like," he said. "They may have to make a change if they get to Old Trafford or Durham, but for Lord's it would be a bit harsh to leave him out.
"The fact it's at his home ground will have a huge impact. He knows the pitch inside out, he just needs the opportunity."
England have been criticised for being overly reliant on Anderson during the first Test, but Gough believes the other bowlers will come to the fore at different times.
"We were too reliant on him on that pitch. Jimmy is the best bower I've ever seen with the new ball in his hand," he said.
"He's improving all the time with the old ball and Trent Bridge is his favourite ground, so the other bowlers will come into their own in the other Tests. Trent Bridge suites Jimmy."
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